Least Common Multiple (LCM) of 120 and 170
The least common multiple (LCM) of 120 and 170 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 170?
First, calculate the GCD of 120 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 170 = 0 remainder 120 |
| 2 | 170 ÷ 120 = 1 remainder 50 |
| 3 | 120 ÷ 50 = 2 remainder 20 |
| 4 | 50 ÷ 20 = 2 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 59 | 944 |
| 188 and 152 | 7144 |
| 138 and 47 | 6486 |
| 170 and 162 | 13770 |
| 56 and 104 | 728 |