Least Common Multiple (LCM) of 97 and 137
The least common multiple (LCM) of 97 and 137 is 13289.
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 97 and 137?
First, calculate the GCD of 97 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 137 = 0 remainder 97 |
| 2 | 137 ÷ 97 = 1 remainder 40 |
| 3 | 97 ÷ 40 = 2 remainder 17 |
| 4 | 40 ÷ 17 = 2 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 110 | 5720 |
| 116 and 89 | 10324 |
| 132 and 79 | 10428 |
| 95 and 185 | 3515 |
| 104 and 157 | 16328 |