{"id":224606,"date":"2025-06-03T10:01:43","date_gmt":"2025-06-03T10:01:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224606"},"modified":"2025-06-03T10:01:46","modified_gmt":"2025-06-03T10:01:46","slug":"kyra-has-a-rock-collection","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/kyra-has-a-rock-collection\/","title":{"rendered":"Kyra has a rock collection"},"content":{"rendered":"\n

Kyra has a rock collection. When she puts her rocks into 2 equal piles, there are no rocks left over. When she puts her rocks into 3 equal piles, there are still no rocks left over. When she puts her rocks into 4 equal piles, there are still no rocks left over. How many rocks could Kyra have<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Kyra could have 12 rocks<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation <\/h3>\n\n\n\n

We are told that Kyra’s rocks can be divided evenly into 2, 3, and 4 equal piles with no rocks left over. This means the number of rocks must be divisible by 2<\/strong>, 3<\/strong>, and 4<\/strong>. In mathematics, a number that is divisible by several other numbers is called a common multiple<\/strong> of those numbers. The least<\/strong> such number is called the Least Common Multiple (LCM)<\/strong>.<\/p>\n\n\n\n

To find the smallest possible number of rocks Kyra could have, we calculate the LCM of 2, 3, and 4.<\/p>\n\n\n\n

Step 1: Prime Factorization<\/h4>\n\n\n\n
    \n
  • 2 is a prime number \u2192 2<\/li>\n\n\n\n
  • 3 is a prime number \u2192 3<\/li>\n\n\n\n
  • 4 = 2 \u00d7 2 = 2\u00b2<\/li>\n<\/ul>\n\n\n\n

    Step 2: Choose the highest powers of each prime<\/h4>\n\n\n\n
      \n
    • From 2: 2\u00b2 (from 4)<\/li>\n\n\n\n
    • From 3: 3\u00b9<\/li>\n<\/ul>\n\n\n\n

      Step 3: Multiply them<\/h4>\n\n\n\n

      LCM = 2\u00b2 \u00d7 3 = 4 \u00d7 3 = 12<\/strong><\/p>\n\n\n\n

      So, the least number of rocks Kyra could have is 12<\/strong>.<\/p>\n\n\n\n

      Let\u2019s verify:<\/p>\n\n\n\n

        \n
      • 12 \u00f7 2 = 6 \u2192 no remainder \u2705<\/li>\n\n\n\n
      • 12 \u00f7 3 = 4 \u2192 no remainder \u2705<\/li>\n\n\n\n
      • 12 \u00f7 4 = 3 \u2192 no remainder \u2705<\/li>\n<\/ul>\n\n\n\n

        Therefore, 12 rocks meet all the conditions.<\/p>\n\n\n\n

        However, the problem says “how many rocks could Kyra have?”<\/strong>, not “what is the smallest number?”<\/strong> This means any multiple of 12<\/strong> would also work (like 24, 36, 48, etc.). But since no specific upper limit is given, the correct answer<\/strong> is the smallest possible<\/strong>, which is 12<\/strong>.<\/p>\n\n\n\n

        In real-world contexts, problems like this teach children about divisibility, multiples, and least common multiples. It\u2019s a great way to apply basic number theory to a scenario that feels concrete and relatable, such as organizing a rock collection.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Kyra has a rock collection. When she puts her rocks into 2 equal piles, there are no rocks left over. When she puts her rocks into 3 equal piles, there are still no rocks left over. When she puts her rocks into 4 equal piles, there are still no rocks left over. How many rocks […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-224606","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224606","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224606"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224606\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224606"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224606"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}