Question

What is the Least Common Multiple?

Answer 1

Least Common Multiple (LCM) : The LCM of two or more given numbers is the least number which is exactly divisible by each of them.

Example : Find the LCM of 3, 4 and 6.

Soln : Multiples of $3=3,6,9,12,15,18,21,24,27,30 \ldots \ldots$.

Multiples of $4=4,8,12,16,20,24,28,32 \ldots \ldots$.

Multiples of $6=6,12,18,24,30 \ldots \ldots$.

$\because$ Common multiples of 3,4 and 6 are $=12,24,36 \ldots \ldots$.

$\therefore \quad$ Least common multiple $=12$ i.e. $\mathrm{LCM}=12$ Ans.

Trick : If the given numbers are of equal base and unequal power then their LCM will be maximum power of the number.

Example : Find the LCM of $2^6, 2^{12}, 2^{19}$

Soln : $\mathrm{LCM}=2^{19}$ Ans.