Least Common Multiple (LCM) of 138 and 97
The least common multiple (LCM) of 138 and 97 is 13386.
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 97?
First, calculate the GCD of 138 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 97 = 1 remainder 41 |
| 2 | 97 ÷ 41 = 2 remainder 15 |
| 3 | 41 ÷ 15 = 2 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 68 | 11764 |
| 136 and 119 | 952 |
| 42 and 122 | 2562 |
| 108 and 121 | 13068 |
| 124 and 24 | 744 |