Least Common Multiple (LCM) of 117 and 149
The least common multiple (LCM) of 117 and 149 is 17433.
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 117 and 149?
First, calculate the GCD of 117 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 149 = 0 remainder 117 |
| 2 | 149 ÷ 117 = 1 remainder 32 |
| 3 | 117 ÷ 32 = 3 remainder 21 |
| 4 | 32 ÷ 21 = 1 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 63 | 1260 |
| 90 and 128 | 5760 |
| 29 and 170 | 4930 |
| 185 and 30 | 1110 |
| 14 and 76 | 532 |