Least Common Multiple (LCM) of 113 and 136
The least common multiple (LCM) of 113 and 136 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 113 and 136?
First, calculate the GCD of 113 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 136 = 0 remainder 113 |
| 2 | 136 ÷ 113 = 1 remainder 23 |
| 3 | 113 ÷ 23 = 4 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 147 | 735 |
| 105 and 135 | 945 |
| 21 and 160 | 3360 |
| 131 and 86 | 11266 |
| 154 and 165 | 2310 |