Q13 of 56 Page 17

Can two numbers have H.C.F as 15 And L.C.M as 175? Give Reasons.

let the numbers be a and b

Now, on prime factorization of 175 = 5 × 5 × 7


And prime factors of 15 = 3 × 5


⇒ H.C.F = product of the smallest power of each common factor


And L.C.M = product of the highest power of each factor involved in the numbers


Now if we take 15 as a number, another number will be 175, but the H.C.F of these two numbers is not 15.


As the L.C.M does not contain 3 as a factor, H.C.F should also not contain 3.


But H.C.F does contain 3.


So, it is not possible to have any two numbers with L.C.M as 175 and H.C.F has 15


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If the product of H.C.F and L.C.M of two natural numbers is 378000, then which of the following can be their H.C.F:

a) 66


b) 130


c) 34


d) 20