Least Common Multiple (LCM) of 137 and 149
The least common multiple (LCM) of 137 and 149 is 20413.
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 149?
First, calculate the GCD of 137 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 149 = 0 remainder 137 |
| 2 | 149 ÷ 137 = 1 remainder 12 |
| 3 | 137 ÷ 12 = 11 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 192 | 1728 |
| 84 and 161 | 1932 |
| 90 and 38 | 1710 |
| 21 and 15 | 105 |
| 33 and 37 | 1221 |