Question

The HCF and LCM of two numbers are 8 and 576 respectively. If one number is 64, find the other number.

Answer 1

Step-by-step explanation:

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The HCF and LCM of two numbers are 8 and 576 respectively. If one number is 64, find the other number.

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☛Let the other number be n.

☛ 64 in terms of prime factors.

64=2×2×2×2×2×2.

☛If 8 is HCF of 64 and n. Then common prime factors between them is 2×2×2=8.

☛Which means n=2×2×2×m, where m is some number.

☛ This means LCM= 2×2×2×2×2×2×m=576.

☛ m=576÷2^6=9.

☛n=2×2×2×3×3=72.

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• What are H.C.F. and L.C.M.?

Ans:- The full forms of H.C.F. and L.C.M. are, Highest Common factor and Least Common Multiple, respectively. The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers.