Least Common Multiple (LCM) of 138 and 160
The least common multiple (LCM) of 138 and 160 is 11040.
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 160?
First, calculate the GCD of 138 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 160 = 0 remainder 138 |
| 2 | 160 ÷ 138 = 1 remainder 22 |
| 3 | 138 ÷ 22 = 6 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 82 | 1968 |
| 176 and 107 | 18832 |
| 99 and 39 | 1287 |
| 68 and 118 | 4012 |
| 74 and 131 | 9694 |