Least Common Multiple (LCM) of 170 and 107
The least common multiple (LCM) of 170 and 107 is 18190.
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 107?
First, calculate the GCD of 170 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 107 = 1 remainder 63 |
| 2 | 107 ÷ 63 = 1 remainder 44 |
| 3 | 63 ÷ 44 = 1 remainder 19 |
| 4 | 44 ÷ 19 = 2 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 54 | 8478 |
| 161 and 136 | 21896 |
| 188 and 200 | 9400 |
| 93 and 98 | 9114 |
| 118 and 160 | 9440 |