Question

Lcm of three natural number 150, 144, and x is 10800. How many value of x are possible?

Answer 1

Answer:

x can have 15 possible values and they are 27, 54, 108, 216, 432, 135, 675, 270, 540, 1080, 2160, 1350, 2700, 5400, 10800.

Step-by-step explanation:

Factors of 150 = 5 * 5 * 3 * 2

Factors of 144 = 3 * 2 * 2 * 3 * 2 * 2

LCM of 144 and 150 = 2⁴ x 3² x 5² = 3600

If the LCM of 144, 150 and x has to be 10,800, we conclude that

x must contain 3³ and any combination of powers of 2^(<=4) and 5^ (<=2)

Hence x shall have the following values:

3³ = 27

27 x 2 = 54

27 x 2² = 108

27 x 2³ = 216

27 x 2⁴ = 432

27 x 5 = 135

27 x 5² = 675

27 x 2 x 5 = 270

27 x 2² x 5 = 540

27 x 2³ x 5 = 1080

27 x 2⁴ x 5 = 2160

27 x 2 X 5² = 1350

27 x 2² x 5² = 2700

27 x 2³ x 5² = 5400

27 x 2⁴ x 5² = 10800

Thus x can have 15 possible values and they are 27, 54, 108, 216, 432, 135, 675, 270, 540, 1080, 2160, 1350, 2700, 5400, 10800.