Example 14 Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case. Least number when divided by 12, 16, 24, 36 & leaves remainder 0
= LCM of 12, 16, 24, 36
So, LCM leaves remainder 0
Now, in the question
We are asked smallest number which leaves remainder 7
So, Required number will be 7 more than LCM
∴ Required number = LCM + 7
Finding LCM of 12, 16, 24, 36
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9 = 144
So, Required Number = LCM + 7
= 144 + 7
= 151

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.