Least Common Multiple (LCM) of 101 and 138
The least common multiple (LCM) of 101 and 138 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 101 and 138?
First, calculate the GCD of 101 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 138 = 0 remainder 101 |
| 2 | 138 ÷ 101 = 1 remainder 37 |
| 3 | 101 ÷ 37 = 2 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 33 | 165 |
| 170 and 41 | 6970 |
| 99 and 14 | 1386 |
| 138 and 181 | 24978 |
| 25 and 67 | 1675 |