Question

# Find the LCM of 18 and 48.

For example: Consider the number 51. It is an odd number. So, it is not divisible by 2. The sum of the digits of 51 is 5 + 1 = 6. Hence, 51 is divisible by 3. Now, $51=3\times 17$ . Now, we take 17. We know, 17 is a prime number. Hence, the prime factors of 51 are 3 and 17.
Now starting with finding the factors of 18. We know 18 is an even number, so it can be written as $18=2\times 9$ . Further we can break 9 as $9=3\times 3$ . Therefore, we can write 18 as $2\times 3\times 3$ .
Now let us move to the factorisation of 48. So, as 48 is a multiple of 16, it must have ${{2}^{4}}$ , i.e., 16 as one of its factors. Also, 48 is divisible by 3 . So, 48 can be written as $48=2\times 2\times 2\times 2\times 3$ .
$LCM\left( 18,48 \right)=2\times 2\times 2\times 2\times 3\times 3=144.$
Note: Be careful while finding the prime factors of each number. Also, it is prescribed that you learn the division method of finding the LCM as well, as it might be helpful. If in case you are asked to find the LCM of two fractions you must use the formula $LCM=\dfrac{LCM\text{ of numerator of the fractions}}{HCF\text{ of the denominator of the fractions}}$.