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 |
|---|---|
| 41 and 72 | 2952 |
| 142 and 91 | 12922 |
| 169 and 144 | 24336 |
| 159 and 141 | 7473 |
| 22 and 118 | 1298 |