Question

the sum of two numbers is 132 and their LCM is 360 . the find the numbers

Answer 1

The lcm of 132 and 360 is 3960.

Steps to find LCM

Find the prime factorization of 132

132 = 2 × 2 × 3 × 11
Find the prime factorization of 360

360 = 2 × 2 × 2 × 3 × 3 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 3 × 3 × 5 × 11LCM = 3960

Answer 2

Answer:

The numbers whose sum is 132 and LCM is 360 is 60 and 72.

Explanation:

What is LCM?

Finding the smallest common multiple between any two or more integers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.

The term LCM stands for the least common multiple or factor of any two or more specified numbers. The least common multiple for the integers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.

The sum of two numbers is 132.

Their LCM is 360.

Let the numbers be 'a' and 'b'.

Therefore ,

a + b = 132

and,

To find the numbers, write the factors of 360

Factors : (2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360)

from the factors of 360, make combinations of two numbers, on adding we get 132.

So,

Case 1:

If we take a= 12, then b= 120

12 +120 = 132

LCM (12,120) = 120

LCM of 12 and 120 is not equal to 360.

so, we have to discard these numbers.

Case 2:

If we take a=60 then b= 72

60 +72 = 132

LCM (60,72) = 360

Thus,

The numbers are 60 and 72.

To learn more about LCM refer to :

brainly.in/question/44031042

brainly.in/question/6191786

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