Least Common Multiple (LCM) of 138 and 101
The least common multiple (LCM) of 138 and 101 is 13938.
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 101?
First, calculate the GCD of 138 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 101 = 1 remainder 37 |
| 2 | 101 ÷ 37 = 2 remainder 27 |
| 3 | 37 ÷ 27 = 1 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 51 | 2805 |
| 180 and 155 | 5580 |
| 36 and 51 | 612 |
| 144 and 69 | 3312 |
| 41 and 42 | 1722 |