Least Common Multiple (LCM) of 109 and 120
The least common multiple (LCM) of 109 and 120 is 13080.
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 109 and 120?
First, calculate the GCD of 109 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 120 = 0 remainder 109 |
| 2 | 120 ÷ 109 = 1 remainder 11 |
| 3 | 109 ÷ 11 = 9 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 87 | 1392 |
| 106 and 88 | 4664 |
| 89 and 80 | 7120 |
| 156 and 178 | 13884 |
| 116 and 119 | 13804 |