Question

The lcm of two numbers is 1200. Show that hcf if these numbers cannot be 500.why ?

Answer 1

This is because the prime factorisation of the large number ie.1200 does not have 500 or multiples of it

Answer 2

LCM- “Lowest Common Multiple” Smallest integer that are the multiple of both numbers.

HCF- “Highest Common Factor” Largest whole number that divides both numbers.

LCM of two numbers is 1200.

Factorizing 1200, we get,

∴ Prime Factors  $= 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 5$

Since we cannot find 500 or multiples of 500 in the factors of 1200, hence 500 cannot be the HCF of the two numbers.