Question

Find the L.C.M. of the following numbers in which one number is the factor of other: (a) $5$ and $20$ (b) $6$ and $18$ (c) $12$ and $48$ (d) $9$ and $45$. What do you observe in the result obtained?

Answer 1

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

Applying Prime Factorization method,

$5=5\times 1$

$20=2\times 2\times 5$

Thus, L.C.M of $5$ and $20$ $=2\times 2\times 5\times 1=20$

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

Applying Prime Factorization method,

$6=2\times 3$

$18=2\times 3\times 3$

Thus, L.C.M of $6$ and $18$ $=2\times 3\times 3=18$

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

Applying Prime Factorization method,

$12=2\times 2\times 3$

$48=2\times 2\times 2\times 2\times 3$

Thus, L.C.M of $12$ and $48$ $=2\times 2\times 2\times 2\times 3=48$

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

Applying Prime Factorization method,

$9=3\times 3$

$45=3\times 3\times 5$

Thus, L.C.M of $9$ and $45$$=3\times 3\times 5=45$

Hence, we can conclude that if one number is the factor of the other, then the L.C.M. of the two numbers will be equal to the greater number.