Least Common Multiple (LCM) of 88 and 113
The least common multiple (LCM) of 88 and 113 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 88 and 113?
First, calculate the GCD of 88 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 113 = 0 remainder 88 |
| 2 | 113 ÷ 88 = 1 remainder 25 |
| 3 | 88 ÷ 25 = 3 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 192 | 384 |
| 185 and 19 | 3515 |
| 172 and 105 | 18060 |
| 187 and 118 | 22066 |
| 137 and 13 | 1781 |