Question

Can 2 numbers have 12 as their h.c.f and 512 as their l.c.m. ? Justify your answer.

Answer 1

•if H.C.F = 12
obviously , then 12 will be a factor of those two numbers.

let the numbers be , 12a and 12b . where , a and b are integers

product of two numbers = H.C.F × L.C.M

12a ×12b = 512 × 12

12 ×12 (ab ) = 512 × 12

ab = 512 × 12 / 12 × 12

ab = 512 / 12

ab = 42.66

which is not possible , because product of two integers can not be in fraction or decimal fraction.

hence , it's not possible .