Question

Find the product of HCF and LCM of 510 and 92.

Answer 1

Hint – In order to solve this problem we need to find LCM and HCF of 510 and 92 and then find the product of the answer obtained in finding LCM and HCF.

Complete step-by-step answer:
The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM (a, b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM (2,3) = 6 and LCM(6,10) = 30.
Highest Common Factor (HCF): The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. Also known as GCD(Greatest Common Divisor). For example, HCF of 4, 6 and 8 is 2.
Prime factorisation of 510=2×3×5×17
Prime factorisation of 92=2×2×23
Hence, LCM of 510, 92=2×3×5×17×2×23=23460 (Since, for two integers 510 and 92, denoted LCM (510, 92), the LCM is the smallest positive integer that is evenly divisible by both 510 and 92 which is 23460)
And HCF of 510, 92=2 (since, 2 gives the largest or greatest factor common to 510, 92)
Now, LCM × HCF =23460×2=46920
Also, 510 × 92=46920
Hence, the answer to this problem is 46920.

Note – To solve this problem we have to take care of the LCM and HCF and always try to do prime factorization. The smallest positive number that is a multiple of two or more numbers is called the LCM and HCF means highest common factor. It means the greatest number which can divide the given numbers.