Least Common Multiple (LCM) of 118 and 138
The least common multiple (LCM) of 118 and 138 is 8142.
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 138?
First, calculate the GCD of 118 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 138 = 0 remainder 118 |
| 2 | 138 ÷ 118 = 1 remainder 20 |
| 3 | 118 ÷ 20 = 5 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 124 | 4712 |
| 198 and 42 | 1386 |
| 58 and 109 | 6322 |
| 146 and 80 | 5840 |
| 146 and 30 | 2190 |