Least Common Multiple (LCM) of 137 and 104
The least common multiple (LCM) of 137 and 104 is 14248.
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 104?
First, calculate the GCD of 137 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 104 = 1 remainder 33 |
| 2 | 104 ÷ 33 = 3 remainder 5 |
| 3 | 33 ÷ 5 = 6 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 16 | 880 |
| 61 and 129 | 7869 |
| 108 and 121 | 13068 |
| 74 and 135 | 9990 |
| 148 and 38 | 2812 |