Least Common Multiple (LCM) of 108 and 119
The least common multiple (LCM) of 108 and 119 is 12852.
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 108 and 119?
First, calculate the GCD of 108 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 119 = 0 remainder 108 |
| 2 | 119 ÷ 108 = 1 remainder 11 |
| 3 | 108 ÷ 11 = 9 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 109 | 4687 |
| 151 and 124 | 18724 |
| 46 and 107 | 4922 |
| 70 and 65 | 910 |
| 23 and 53 | 1219 |