Question

Find the $LCM$ and $HCF$of the following integers by applying the prime factorization method.

$12,15$and $21$

Answer 1

Solve for the H.C.F and L.C.M of the given numbers

The prime factors of the given numbers are

$12=2\times 2\times 3=2^2\times 3^1$

$15=3\times 5$ $=3^1\times 5^1$

$21=3\times 7$ $=3^1\times 7^1$

The common factor $=3$

$\therefore$H.C.F.$(12,15,21)=3$

Now calculating the Least Common Multiple (LCM) of $12,15$ and $21$

$\therefore$L.C.M.$(12,15,21)=2^2\times 5^1\times 3^1\times 7^1$

$\Rightarrow$L.C.M.$(12,15,21)=420$

Hence, the L.C.M. is $420$ and H.C.F. is $3$.