Find the HCF and LCM of 35,40,50 using the division method
The correct answer and explanation is:
To find the HCF and LCM of 35, 40, and 50 using the division method, follow the steps below:
Step 1: Division Method for HCF
The division method involves dividing the numbers by their common divisors until only the HCF remains.
- Divide 50 by 35. The quotient is 1 and the remainder is 15. 50÷35=1remainder1550 \div 35 = 1 \quad \text{remainder} \quad 15
- Divide 35 by 15. The quotient is 2 and the remainder is 5. 35÷15=2remainder535 \div 15 = 2 \quad \text{remainder} \quad 5
- Divide 15 by 5. The quotient is 3 and the remainder is 0. 15÷5=3remainder015 \div 5 = 3 \quad \text{remainder} \quad 0
The remainder is now zero, so the divisor at this step (which is 5) is the HCF.
Thus, the HCF of 35, 40, and 50 is 5.
Step 2: Division Method for LCM
The LCM can be found using the relation between LCM and HCF: LCM(a,b,c)=a×b×cHCF(a,b,c)\text{LCM}(a, b, c) = \frac{a \times b \times c}{\text{HCF}(a, b, c)}
Given that the HCF of 35, 40, and 50 is 5, we can now calculate the LCM: LCM(35,40,50)=35×40×505=700005=14000\text{LCM}(35, 40, 50) = \frac{35 \times 40 \times 50}{5} = \frac{70000}{5} = 14000
Thus, the LCM of 35, 40, and 50 is 14,000.
Explanation:
The HCF is the largest number that divides all the given numbers without leaving a remainder. In this case, 5 is the largest number that divides 35, 40, and 50 without a remainder. The LCM is the smallest number that all the given numbers divide into evenly. Using the formula relating HCF and LCM, we calculate the LCM as 14,000.