Question

LCM of 8, 16, 24 and 32 is
A. 96
B. 72
C. 108
D. 128

Answer 1

Hint:Here they have provided four numbers. Thus we need to find the least number which is a multiple of all these four numbers. As all the given numbers have common factors, we will go for the prime factorization of these. Thus LCM will be the product of each of the distinct prime factors with its greatest number of occurrence times.

Complete step-by-step answer:
Least common multiple (LCM) of numbers a, b is defined to be the least number which is a multiple of both a and b.
Let us prime factorize each of the numbers.
$8=2\times 2\times 2$
The next number,
$16=2\times 2\times 2\times 2$
Now $24=2\times 2\times 2\times 3$
And $32=2\times 2\times 2\times 2\times 2$
LCM = product of each distinct factor its largest occurrence times among all factorizations.
Largest occurrence of 2 among all factorizations is 5. Thus 2 will get multiplied 5 times.
Largest occurrence of 3 is one.
Thus LCM (8, 16, 24, 32)$=2\times 2\times 2\times 2\times 2\times 3=96$
LCM of 8, 16, 24 and 32 is 96.

So, the correct answer is “Option A”.

Note:Prime factorization of a number has to be done by checking all the prime factors are either a factor of given number or not. We start by the smallest prime number 2, then we check for 3 and then 5 etc. LCM and HCF are two factors of numbers which decide how much connected those numbers are. HCF (Highest Common Factor) gives the greatest factor which is common to all the numbers under consideration. LCM and HCF can be found for a list of numbers starting from a couple of them.