Question

18. The lcm and hcf of two numbers are 2970 and 30 respectively. Prime factors of the product of two numbers are: a. 2, 3, 5, 11 b. 2, 3, 7, 11 c. 2, 4, 5, 11 d. 2, 3, 7, 13

Answer 1

As given ,

H.C.F= 2970

L.C.M=30

As we know , H.C.F × L.C.M=Product of two numbers

→Product of two numbers = 2970 × 30

                            2970=2×3×3×3×5×11

                            30=2×3×5

Combining them, 2970×30=[2×3×3×3×5×11]×[2×3×5]

So, prime factors of the product of two numbers are: a. 2, 3, 5, 11

Answer 2

Thank you for asking this question: Here is your answer:

Solution is 2,3,5,11

Factors of [2970] = 2*3*5*3*3*11

Factors of [30] =     2*3*5HCF = 2*3*5 = 30

LCM = 2*3*5*32*11 = 30*99 = 2970

2970 = 2 * 5 * 3 * 3 * 11

30 = 2*3*5

LCM of the two numbers  = 2*3*3*3*5*11 = 2970

So the prime factors are = 2,3,5,11

The correct answer is option A