Find the least number when divide by 25, 45, 60 leaves reminder 20.
2) Find the least number which when divided by 18, 12, 24 leaves a reminder of 16, 10, 22 respectively.
Can U help me to find the answer.
LCM(25,45,60) = 900
So, 920 will do the trick.
70 = 16 + 3*18 = 10 + 5*12 = 22 + 2*24
Certainly! I'll explain how to find the answers to both of these questions step-by-step.
1) To find the least number that, when divided by 25, 45, and 60, leaves a remainder of 20, you can follow these steps:
a) Start by finding the LCM (Least Common Multiple) of 25, 45, and 60. The LCM is the smallest number that is divisible by all three numbers.
LCM(25, 45, 60) = 900
b) Now, subtract the remainder (20) from the LCM to find the least number.
Least number = LCM - Remainder = 900 - 20 = 880
Therefore, the least number that satisfies the given conditions is 880.
2) Similarly, to find the least number that, when divided by 18, 12, and 24, leaves remainders of 16, 10, and 22 respectively, follow these steps:
a) Find the LCM of 18, 12, and 24.
LCM(18, 12, 24) = 72
b) Subtract the respective remainders from the LCM to find the least number.
Least number = LCM - Remainders = 72 - (16, 10, 22) = (56, 62, 50)
Therefore, the least number that satisfies the given conditions is 56.
I hope this helps! Let me know if you have any further questions.