Question

the lcm of 2³×3²×5×11,2⁴×3⁴×5²×7,and2⁵×3³×5³×7²×11​

Answer 1

remember if we have to take the lcm of anything we have to first

1. take the highest exponent out of every no. from the number's prime factorisation and have multiply them

lcm =2^5× 3^4× 5^3× 7^2× 11

=32×81×125×49×11

=18,11,04,000

Answer 2

Given: 2³×3²×5×11, 2⁴×3⁴×5²×7 and 2⁵×3³×5³×7²×11​

To find: LCM of the given expressions

Solution:

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

∴ 2³×3²×5×11

∴ 2⁴×3⁴×5²×7 and

∴ 2⁵×3³×5³×7²×11​

We know that LCM of given numbers is the product of maximum frequencies of all the numbers involved in all prime factorizations.

∴ LCM = 2⁵ × 3⁴ × 5³ × 7² × 11

           = 32 × 81 × 125 × 49 × 11

            = 174636000

Hence, LCM of the given expressions is 174636000