Least Common Multiple (LCM) of 138 and 119
The least common multiple (LCM) of 138 and 119 is 16422.
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 138 and 119?
First, calculate the GCD of 138 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 119 = 1 remainder 19 |
| 2 | 119 ÷ 19 = 6 remainder 5 |
| 3 | 19 ÷ 5 = 3 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 118 | 20178 |
| 53 and 66 | 3498 |
| 144 and 52 | 1872 |
| 99 and 59 | 5841 |
| 163 and 22 | 3586 |