Least Common Multiple (LCM) of 120 and 17
The least common multiple (LCM) of 120 and 17 is 2040.
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 120 and 17?
First, calculate the GCD of 120 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 17 = 7 remainder 1 |
| 2 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 102 | 8772 |
| 188 and 171 | 32148 |
| 15 and 138 | 690 |
| 100 and 199 | 19900 |
| 10 and 55 | 110 |