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

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)

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

Answer: (b)

LCM of 21, 36 and 66

∴ LCM = 3 × 2 × 7 × 6 × 11

= 3 × 3 × 2 × 2 × 7 × 11

∴ Required number

= $3^2 × 2^2 × 7^2 × 11^2$

= 213444

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