Question

The L.C.M. of 2^3 x3^2 x5x11, 2^3 x3^3x5^2 x7^2 and 2^5 x3^3 x5^3 x7^2 x11 is

Answer 1

The LCM of the numbers  2^3 x 3^2 x 5 x 11, 2^3 x 3^3 x 5^2 x 7^2 and 2^5 x 3^3 x 5^3 x 7^2 x 11 is :

2^5 x 3^3 x 5^3 x 7^2 x 11

= 58212000 : Ans

Hope I helped

Answer 2

Given: $2^{3}$ × $3^{2}$ × $5$ × $11$, $2^{3}$ × $3^{3}$ × $5^{2}$ × $7^{2}$ and $2^{5}$ × $3^{3}$ × $5^{3}$ × $7^{2}$ × $11$

To find: LCM of the given expressions

Solution:

We have been given three expressions representing three numbers as the product of their prime factors.

∴ $2^{3}$ × $3^{2}$ × $5$ × $11$

∴  $2^{3}$ × $3^{3}$ × $5^{2}$ × $7^{2}$

∴  $2^{5}$ × $3^{3}$ × $5^{3}$ × $7^{2}$ × $11$

We know that LCM is the product of maximum frequencies of all the integers(positive) involved in all prime factorizations.

∴ LCM =  $2^{5}$ × $3^{3}$ ×  $5^{3}$ × $7^{2}$ ×  $11$   [2, 3, 5, 7 and 11 are involved in given expressions and their maximum frequencies have been taken to find LCM]

           = 32 × 27 × 125 × 49 × 11

           = 58212000

Hence, LCM of the given expressions is 58212000.