Least Common Multiple (LCM) of 119 and 129
The least common multiple (LCM) of 119 and 129 is 15351.
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 119 and 129?
First, calculate the GCD of 119 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 129 = 0 remainder 119 |
| 2 | 129 ÷ 119 = 1 remainder 10 |
| 3 | 119 ÷ 10 = 11 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 161 | 23345 |
| 168 and 163 | 27384 |
| 80 and 111 | 8880 |
| 18 and 71 | 1278 |
| 35 and 64 | 2240 |