Least Common Multiple (LCM) of 136 and 113
The least common multiple (LCM) of 136 and 113 is 15368.
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 136 and 113?
First, calculate the GCD of 136 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 113 = 1 remainder 23 |
| 2 | 113 ÷ 23 = 4 remainder 21 |
| 3 | 23 ÷ 21 = 1 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 74 | 3700 |
| 21 and 199 | 4179 |
| 60 and 23 | 1380 |
| 57 and 12 | 228 |
| 200 and 157 | 31400 |