model 2 find lcm of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Using Rule 5,

When a number is divided by P, Q or R leaving remainders X, Y or Z respectively such that the difference between divisor and remainder in each case is same i.e., (P – X) = (Q – Y) = (R – Z) = T (say) then that (least) number must be in the form of (K – T), where K is LCM of P, Q and R

The smallest number divisible by 12 or 10 or 8

= LCM of 12, 10 and 8 = 120

⇒ Required number =120 + 6 = 126

Answer: (c)

The LCM of 5, 6, 7 and 8 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.

Now, 840 k + 3 = 93 × 9 k + (3k + 3)

When k = 2, 3k + 3 = 9, which is divisible by 9.

∴ Required number = 840 × 2 + 3 = 1683

Answer: (c)

Required number = (LCM of 24, 32, 36 and 54) – 5

Now,

LCM = 2 × 2 × 2 × 3 × 3 × 3 × 4 = 864

∴ Required number = 864 – 5

= 859