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

A.

216

B.

389

C.

443

D.

548

Answer with explanation

Answer: Option DExplanation

Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.

**(OR)**

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 the 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.

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Mithun Choudhury says

please explain how to solvw

Mithun Choudhury says

explain how to solve

Saran Harika says

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 the 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.

pooja says

how l c m is calculated

exams says

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 the 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.

pooja says

please help