Question

Find the smallest number which when divided by 18,12 and 24

leaves the remainder of 16, 10 and 22 respectively.​

Answer 1

Answer:

70

Step-by-step explanation:

A number when divided by divisors 18,12,24 should leave a remainder os 16,10 and 22 respectively.

When you see the divisors and the remainders, the remainders are exactly 2 less than the divisors.

the easiest of doing this problem is find out the LCM of the three numbers and reduce it by 2. that will be the smallest number as required by the question. the LCM will be divisible by all the three numbers and when you reduce 2 from the LCM the remainder will be two less than the divisors.

The LCM for three numbers 18, 12 and 24 is 72 . when you reduce 2 from LCM 72 you will get the answer as 70.

Answer 2

Given: Numbers 18, 12 and 24

To find: Smallest number which when divided by 18, 12 and 24 leaves remainder 16, 10 and 22 respectively.

Solution: The smallest number when divided by 18, 12 and 24 leaving remainder 16, 10 and 22 :-

Subtract the given remainders from the numbers:

18 - 16 = 2, 12 - 10 = 2 and 24 - 22 = 2

Therefore, the required number will be 2 less than the L.C.M. of 18, 12 and 24

Finding L.C.M. using prime factorization method

18 = 2 x 3 x 3

12 = 2 x 2 x 3

24 = 2 x 2 x 2 x 3

L.C.M. of 18, 12 and 24 is 2 x 2 x 2 x 3 x 3 = 72

Hence, the required number will be 72 - 2 = 70 which when divided by 18, 12 and 24 leaves remainder 16, 10 and 22 respectively.