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

Answer: (c)

Using Rule 8,

Greatest n digit number which when divided by three numbers P, Q, R leaves no remainder will be

Required Number = (n – digit greatest number) – R

R is the remainder obtained on dividing greatest n digit number by L.C.M of P, Q, R.

LCM of 10, 15 and 20 = 60

Largest 4-digit number = 9999

∴ 166$39/60$ = 9999

∴ Required number = 9999 – 39

= 9960

Answer: (c)

LCM of 25, 50 and 75 = 150

On dividing 43582 by 150, remainder = 82

290$82/150$ = 43582

∴ Required number = 43582 + (150 – 82)

= 43650

Answer: (c)

∴ 60 = 2 × 2 × 3 × 5

i.e., Numbers = 2, 3, 4 and 5

∴ Required sum = 2 + 3 + 4 + 5 = 14

Answer: (a)

The LCM of 6, 12 and 18 = 36 = $6^2$

Answer: (c)

LCM of 3, 5, 6, 8, 10 and 12 = 120

∴ Required number = 120x + 2, which is exactly divisible by 13.

120x + 2 = 13 × 9x + 3x + 2

Clearly 3x + 2 should be divisible by 13.

For x=8,3x + 2 is divisible by 13.

∴ Required number = 120x + 2 = 120 × 8 + 2

= 960 + 2 = 962

Answer: (a)

Using Rule 4,

i.e. When a number is divided by x, y or z leaving same remainder ‘R’ in each case then that number must be K + R where k is LCM of x, y and z.

Required number = (LCM of 15, 20, 36 and 48) + 3

∴ LCM = 2 × 2 × 3 × 5 × 3 × 4 = 720

∴ Required number = 720 + 3 = 723