model 2 find lcm of numbers Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

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 the 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

Here 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3

∴ The required number = LCM of (4, 5, 6) – 3

= 60 – 3 = 57

Answer: (c)

LCM of 4, 6, 10, 15 = 60

Least number of 6 digits = 100000

The least number of 6 digits which is exactly divisible by 60 = 100000 + (60 – 40) = 100020

∴ Required number (N) = 100020 + 2 = 100022

Hence, the sum of digits = 1 + 0 + 0 + 0 + 2 + 2 = 5

Answer: (c)

LCM of 4, 6, 8, 9

∴ LCM = 2 × 2 × 3 × 2 × 3 = 72

∴ Required number = 72, because it is exactly divisible by 4, 6, 8 and 9 and it leaves remainder 7 when divided by 13.

Answer: (a)

We find LCM of = 10, 16, 24

∴ LCM = $2^2$ × $2^2$ × 3 × 5

∴ Required number

= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

= 3600

Answer: (d)

Using Rule 5,

LCM of 15, 20 and 35 = 420

∴ Required least number = 420 + 8 = 428