Question

The product of three numbers is 1620. If the HCF of any two out
of the three numbers is 3, what is their LCM?
(1) 180
(2) 135
(3) 90
(4) 270
(5) 288

Answer 1

factors of 1620  = (2 x  3)  x  (3  x  3  x 3)  x  (2  x 5)

HCF of two numbers  = 3

So I took  6 x 9 x 10 = 1620

LCM = 270

Answer 2

Solution:

Product of three numbers = 1620

Let the three numbers be x, y,z.

→HCF(x,y)= HCF(y,z)=HCF(z,x)=3

The prime factorization of 1620 is

→1620 = 2 ×2 ×3×3×3×3×5

→If we make three number among the factor of 1620 = 2 ×2 ×3×3×3×3×5 such that HCF of any two out  of the three numbers is 3, one of the group of these numbers is (9,12,15) other being (3,15,36).

LCM (9,12,15)=

Now, 9 = 3 × 3, 12 = 2×2×3, 15 = 3 × 5

LCM(9,12,15) = 3 × 3×2×2×5=180

LCM(3,36,15),

→ 3 = 3 × 1, 36 = 3×3×2×2, 15 = 3×5

LCM (3,36,15) = 3 × 3×2×2×5=180

So, LCM of those three numbers whose product is 1620 and HCF of any two out of the three numbers is 3 is 180.→ Option (1) 180