Question

can two number have 18 as their HCF and 380 as their LCM? Give reasons.

Answer 1

No...two numbers cannot have their hcf as 18 and lcm as 380....this is because of the fundamental theorem of arithmetic that states every composite number has a unique prime factorisation apart from the order in which they appear....also the formula hcf(a,b)*lcm(a,b)=a*b....so no two numbers can have the same lcm and hcf

Answer 2

Answer:

this is a very nice question

the question is "can two number have 18 as their hcf and numbers 380 as their lcm?"

so for solving this sum ,we must recall a property..............

→ lcm is a mutiple of hcf ←

here , we see that 380 is not multiple of 18

∴two no. cant have  18 as their hcf and numbers 380 as their lcm