Question

Can two numbers have 16 as the hcf and 280 as there lcm ? Give reasons in support of your answer

Answer 1

if lcm is divisible by hcf then it is possible to have the numbers.

280 is not divisible by 16.so it is not possible

Answer 2

Let the two numbers be x and y.

∴ LCM is divisible by x and y and x and y are divisible by HCF.

∴ LCM is divisible by HCF.

Given, LCM = 280 and HCF = 16

Since 16 do not divide 280.

∴ Two numbers cannot have16 as their HCF and 280 as their LCM.