Least Common Multiple (LCM) of 15 and 118
The least common multiple (LCM) of 15 and 118 is 1770.
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 15 and 118?
First, calculate the GCD of 15 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 118 = 0 remainder 15 |
| 2 | 118 ÷ 15 = 7 remainder 13 |
| 3 | 15 ÷ 13 = 1 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 89 | 12638 |
| 159 and 131 | 20829 |
| 187 and 99 | 1683 |
| 43 and 108 | 4644 |
| 186 and 126 | 3906 |