Least Common Multiple (LCM) of 113 and 88
The least common multiple (LCM) of 113 and 88 is 9944.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 88?
First, calculate the GCD of 113 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 88 = 1 remainder 25 |
| 2 | 88 ÷ 25 = 3 remainder 13 |
| 3 | 25 ÷ 13 = 1 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 132 | 3564 |
| 36 and 81 | 324 |
| 100 and 69 | 6900 |
| 131 and 153 | 20043 |
| 90 and 134 | 6030 |