Least Common Multiple (LCM) of 61 and 138
The least common multiple (LCM) of 61 and 138 is 8418.
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 61 and 138?
First, calculate the GCD of 61 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 138 = 0 remainder 61 |
| 2 | 138 ÷ 61 = 2 remainder 16 |
| 3 | 61 ÷ 16 = 3 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 36 | 3204 |
| 142 and 100 | 7100 |
| 84 and 195 | 5460 |
| 108 and 120 | 1080 |
| 63 and 152 | 9576 |