Question

Find the LCM of 21, 35 and 48.

Answer 1

Hint – In this particular question use the concept that first of all calculate all the prime factors of the given number for example the prime factors of 10 are (1, 2 and 5), prime factors are those which are divided by 1 or itself so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given numbers are 21, 35 and 48.
We have to find out the L.C.M of these numbers.
L.C.M is called the least common multiple.
The least common multiple (LCM) of any two numbers or more than two numbers is calculated as first list all the prime factors of each number, then multiply each factor the greatest number of times it occurs in the numbers. If the same factor occurs more than once in the given numbers then we have to multiply the factor the greatest number of times it occurs.
Therefore, first calculate the factors of the first number i.e. 21. So, the factors of 21 are,
$21 = 1 \times 3 \times 7$
Now calculate the factors of the second number i.e. 35. So, the factors of 35 are
$35 = 1 \times 5 \times 7$
Now calculate the factors of the third number i.e. 48. So, the factors of 48 are
$48 = 1 \times 2 \times 2 \times 2 \times 2 \times 3$
The L.C.M of the given numbers according to above definition is calculated as
L.C.M = $1 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \times 7$ = 1680
So the L.C.M of 21, 35 and 48 is = 1680
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that the LCM of two numbers or greater than two numbers is calculated as first list all the prime factors of each number, then multiply each factor the greatest number of times it occurs in the numbers. If the same factor occurs more than once in the given numbers then we have to multiply the greatest number of times it occurs, so first find out all the prime factors of each number as above then find the LCM using the above written property.