Least Common Multiple (LCM) of 119 and 107
The least common multiple (LCM) of 119 and 107 is 12733.
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 107?
First, calculate the GCD of 119 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 107 = 1 remainder 12 |
| 2 | 107 ÷ 12 = 8 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 172 | 8772 |
| 174 and 101 | 17574 |
| 87 and 36 | 1044 |
| 59 and 140 | 8260 |
| 90 and 160 | 1440 |