Least Common Multiple (LCM) of 138 and 114
The least common multiple (LCM) of 138 and 114 is 2622.
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 114?
First, calculate the GCD of 138 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 114 = 1 remainder 24 |
| 2 | 114 ÷ 24 = 4 remainder 18 |
| 3 | 24 ÷ 18 = 1 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 145 | 1740 |
| 38 and 72 | 1368 |
| 11 and 171 | 1881 |
| 112 and 176 | 1232 |
| 123 and 152 | 18696 |