Least Common Multiple (LCM) of 118 and 133
The least common multiple (LCM) of 118 and 133 is 15694.
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 118 and 133?
First, calculate the GCD of 118 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 133 = 0 remainder 118 |
| 2 | 133 ÷ 118 = 1 remainder 15 |
| 3 | 118 ÷ 15 = 7 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 19 | 2432 |
| 22 and 12 | 132 |
| 59 and 178 | 10502 |
| 118 and 82 | 4838 |
| 159 and 108 | 5724 |