Question

If both 11^2 and 7^2 are factors of the number a x 4^3 x 66^6 x 56^11, then what is the smallest possible value of a?

Answer 1

Answer:

Step-by-step explanation:

a should be number which is divisible by both 11² and 7²

therefore lcm of 11² and 7² = 121×49=5929 therefore 5929 is the smallest possible value of a we took a as lcm of 7 and 11 square as the remaining numbers were not divisible by nor 11 neither 7

Answer 2

Given : both 7² and 11² are the factors of the number (a x 4³ x 66⁶ x 56¹¹)

To Find :  smallest possible value of a

Solution:

a x 4³ x 66⁶ x 56¹¹

= a  x 4³ x (6 x 11)⁶ x (7x8)¹¹

=  a  x 4³ x  6⁶ x 11⁶ x  7¹¹

=  a  x 4³ x  6⁶ x 11² x 11⁴ x  7² x 7⁹

both 7² and 11² are already the factors of the number

Hence a  can be 1

Smallest possible value of a is 1

Smallest possible value of a = 1

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