Least Common Multiple (LCM) of 138 and 158
The least common multiple (LCM) of 138 and 158 is 10902.
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 158?
First, calculate the GCD of 138 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 158 = 0 remainder 138 |
| 2 | 158 ÷ 138 = 1 remainder 20 |
| 3 | 138 ÷ 20 = 6 remainder 18 |
| 4 | 20 ÷ 18 = 1 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 163 | 32111 |
| 12 and 164 | 492 |
| 101 and 175 | 17675 |
| 128 and 160 | 640 |
| 189 and 135 | 945 |