There are 4 numbers, The HCF of each pair is 7 and the LCM of all the

1.	There are 4 numbers, The HCF of each pair is 7 and the LCM of all the numbers is 1470. What is the product of the 4 numbers ?(a) 504210 (b) 502410 (c) 504120 (d) 501420
Answer» (a) 504210. Since the HCF of each pair = 7, let the four numbers be 7a, 7b, 7c, 7d. Also, LCM = abcd × HCF ⇒ abcd \(\frac{1470}{7} = 210\) ∴ Product of the numbers = 7a × 7b × 7c × 7d = 7⁴ × abcd = 7⁴ × 210 = 504210.

There are 4 numbers, The HCF of each pair is 7 and the LCM of all the numbers is 1470. What is the product of the 4 numbers ?(a) 504210 (b) 502410 (c) 504120 (d) 501420

Answer»

(a) 504210.

Since the HCF of each pair = 7, let the four numbers be 7a, 7b, 7c, 7d.

Also, LCM = abcd × HCF

⇒ abcd \(\frac{1470}{7} = 210\)

∴ Product of the numbers

= 7a × 7b × 7c × 7d

= 7⁴ × abcd = 7⁴ × 210 = 504210.