The least common multiple of 20 25 and 45 is
The Correct Answer and Explanation is:
To find the least common multiple (LCM) of 20, 25, and 45, we first need to identify the prime factorization of each number:
- 20 = 2² * 5
- 25 = 5²
- 45 = 3² * 5
Step 1: Identify all the prime factors
The prime factors involved are 2, 3, and 5. For the LCM, we take the highest power of each prime factor from the factorizations:
- The highest power of 2 is 2² (from 20).
- The highest power of 3 is 3² (from 45).
- The highest power of 5 is 5² (from 25).
Step 2: Multiply the highest powers
Now, we multiply these highest powers together to get the LCM:
LCM = 2² * 3² * 5²
LCM = 4 * 9 * 25
LCM = 900
Step 3: Verify by checking divisibility
To verify, we check if 900 is divisible by 20, 25, and 45:
- 900 ÷ 20 = 45
- 900 ÷ 25 = 36
- 900 ÷ 45 = 20
Since 900 is divisible by all three numbers, the LCM of 20, 25, and 45 is indeed 900.
Conclusion:
The least common multiple of 20, 25, and 45 is 900.
