Least Common Multiple (LCM) of 113 and 118
The least common multiple (LCM) of 113 and 118 is 13334.
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 118?
First, calculate the GCD of 113 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 118 = 0 remainder 113 |
| 2 | 118 ÷ 113 = 1 remainder 5 |
| 3 | 113 ÷ 5 = 22 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 45 | 1440 |
| 53 and 181 | 9593 |
| 72 and 164 | 2952 |
| 69 and 36 | 828 |
| 28 and 137 | 3836 |