Least Common Multiple (LCM) of 119 and 138
The least common multiple (LCM) of 119 and 138 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 119 and 138?
First, calculate the GCD of 119 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 138 = 0 remainder 119 |
| 2 | 138 ÷ 119 = 1 remainder 19 |
| 3 | 119 ÷ 19 = 6 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 26 | 2496 |
| 189 and 36 | 756 |
| 56 and 35 | 280 |
| 35 and 129 | 4515 |
| 143 and 72 | 10296 |