Question

Q.- The least number which when divided by 12 15 20 and 54 leaves in each case a remainder of 8 is:

a-582.
b-548.
c-854.
d-584

Answer 1

LCM of 12, 15, 20, 54

12 = 2 x 2 x 3
15 = 3 x 5
20 = 2 x 2 x 5
54 = 2 x 3 x 3 x 3

LCM = 27 x 4 x 5 = 27 x 20
= 540

ADD 8
= 540 + 8 = 548

Therefore, the answer is 548 that is 'B'

Answer 2

Answer:

Option B is correct.i.e., 548

Step-by-step explanation:

Given numbers are 12 , 15 , 20 , 54

To Find: least no. which is divided by given nos. and leaves remainder 8

Least no which is divisible by all given no is LCM of all nos.

LCM means least common multiple.

First we find LCM of 12 , 15 , 20 , 54  by prime factorization method

12 = 2 × 2 × 3

15 = 3 × 5

20 = 2 × 2 × 5

54 = 2 × 3 × 3 × 3

LCM( 12, 15 , 20 , 54 ) = 2 × 2 × 3 × 3 × 3 × 5 = 540

To find the required no. we add 8 to LCM

⇒ Required No. = 540 + 8 = 548

Thus, 548 is the least no which when divided by 12 15 20 and 54 leaves in each case a remainder of 8.

Therefore, Option B is correct.i.e., 548