Least Common Multiple (LCM) of 138 and 90
The least common multiple (LCM) of 138 and 90 is 2070.
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 90?
First, calculate the GCD of 138 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 90 = 1 remainder 48 |
| 2 | 90 ÷ 48 = 1 remainder 42 |
| 3 | 48 ÷ 42 = 1 remainder 6 |
| 4 | 42 ÷ 6 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 22 | 1496 |
| 32 and 46 | 736 |
| 150 and 45 | 450 |
| 172 and 173 | 29756 |
| 180 and 163 | 29340 |