Least Common Multiple (LCM) of 170 and 177
The least common multiple (LCM) of 170 and 177 is 30090.
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 170 and 177?
First, calculate the GCD of 170 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 177 = 0 remainder 170 |
| 2 | 177 ÷ 170 = 1 remainder 7 |
| 3 | 170 ÷ 7 = 24 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 57 | 9975 |
| 121 and 160 | 19360 |
| 142 and 176 | 12496 |
| 140 and 33 | 4620 |
| 200 and 177 | 35400 |