Least Common Multiple (LCM) of 115 and 149
The least common multiple (LCM) of 115 and 149 is 17135.
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 115 and 149?
First, calculate the GCD of 115 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 149 = 0 remainder 115 |
| 2 | 149 ÷ 115 = 1 remainder 34 |
| 3 | 115 ÷ 34 = 3 remainder 13 |
| 4 | 34 ÷ 13 = 2 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 109 | 16677 |
| 53 and 60 | 3180 |
| 92 and 110 | 5060 |
| 141 and 156 | 7332 |
| 112 and 91 | 1456 |