Least Common Multiple (LCM) of 60 and 170
The least common multiple (LCM) of 60 and 170 is 1020.
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 60 and 170?
First, calculate the GCD of 60 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 170 = 0 remainder 60 |
| 2 | 170 ÷ 60 = 2 remainder 50 |
| 3 | 60 ÷ 50 = 1 remainder 10 |
| 4 | 50 ÷ 10 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 47 | 7755 |
| 57 and 115 | 6555 |
| 188 and 49 | 9212 |
| 70 and 51 | 3570 |
| 111 and 30 | 1110 |