Least Common Multiple (LCM) of 137 and 98
The least common multiple (LCM) of 137 and 98 is 13426.
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 137 and 98?
First, calculate the GCD of 137 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 98 = 1 remainder 39 |
| 2 | 98 ÷ 39 = 2 remainder 20 |
| 3 | 39 ÷ 20 = 1 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 87 | 957 |
| 38 and 18 | 342 |
| 48 and 137 | 6576 |
| 78 and 60 | 780 |
| 120 and 59 | 7080 |