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 |
|---|---|
| 38 and 86 | 1634 |
| 200 and 64 | 1600 |
| 158 and 32 | 2528 |
| 21 and 101 | 2121 |
| 137 and 151 | 20687 |