If 132300 = 2 2 × 3 3 × 5 2 × a b , then which of the following is true ? Options: A . &nbspa=2b B . &nbspa+b=8 C . &nbsp LCM of a and b is 14. D . &nbspa=b

Answer: Option C : C 132300 = 2 2 × 3 3 × 5 2 × a b By fundamental theorem of arithmetic, 132300 can be written as 2 2 × 3 3 × 5 2 × 7 2 . On comparison, we get a = 7 and b = 2. LCM of 7 and 2 is 14.

If 132300=22×33×52×ab, then which of the following is true ?

Question

132300 = 2^{2} \times 3^{3} \times 5^{2} \times a^{b},

then which of the following is true ?

Options:

A . a=2b

B . a+b=8

C . LCM of a and b is 14.

D . a=b

Answer: Option C
:
C

132300 = 2^{2} \times 3^{3} \times 5^{2} \times a^{b}

By fundamental theorem of arithmetic, 132300 can be written as

2^{2} \times 3^{3} \times 5^{2} \times 7^{2} .

On comparison, we get

a = 7

and

b = 2.

LCM of 7 and 2 is 14.

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