Find the least number which when divide by 16,18 and 24 leave remainder 6 in each case
Answers
Answer:
To find the least number which is divisible by a given set of numbers , we must always find their LCM .
Which means , we need to find the LCM of 16 , 18 and 24 .
LCM of 16 , 18 and 24 :
= 16 ÷ 2 , 18 ÷ 2 , 24 ÷ 2 ( dividing by 2 )
= 8 , 9 , 12
= 8 ÷ 2 , 9 , 12 ÷ 2 ( dividing by 2 )
= 4 , 9 , 6
= 4 ÷ 2 , 9 , 6 ÷ 2 ( dividing by 2 )
= 2 , 9 , 3
= 2 , 9 ÷ 3 , 3 ÷ 3 ( dividing by 3 )
= 2 , 3 , 1
= 2 ÷ 2 , 3 , 1 ( dividing by 2 )
= 1 , 3 , 1
= 1 , 3 ÷ 3 , 1 ( dividing by 3 )
= 1 , 1 , 1
LCM of 16 , 18 and 24 = 2 × 2 × 2 × 3 × 2 × 3 = 144
LCM of 16 , 18 and 24 = 144
So if 144 divided 16 , 18 and 24 gives remainder 0 , then :
144 - 6 will give remainder 6 .
144 - 6 = 138 .
Therefore , the least number which when divided by 16 , 18 and 24 gives remainder 6 is = 138 .
Hope you find my answer useful!!