Question

Find the L.C.M of the following numbers: (a) $9$ and $4$ (b) $12$ and $5$ (c) $6$ and $5$ (d) $15$ and $4$ Observe a common property in the obtained L.C.Ms. Is L.C.M. the product of two numbers each case?

Answer 1

Step 1: (a) Find L.C.M.

Applying Prime Factorization method,

$9=3\times 3$

$4=2\times 2$

Thus, L.C.M of $9$ and $4$ $=2\times 2\times 3\times 3=36$

Step 2: (b) Find L.C.M.

Applying Prime Factorization method,

$12=2\times 2\times 3$

$5=5\times 1$

Thus, L.C.M of $12$ and $5$ $=2\times 2\times 3\times 5=60$

Step 3: (c) Find L.C.M.

Applying Prime Factorization method,

$6=2\times 3$

$5=5\times 1$

Thus, L.C.M of $6$ and $5$ $=2\times 3\times 5=30$

Step 4: (d) Find L.C.M.

Applying Prime Factorization method,

$15=3\times 5$

$4=2\times 2$

Thus, L.C.M of $15$ and $4$ $=2\times 2\times 3\times 5=60$

Hence, the L.C.M. is equal to the product of given two numbers in each case