Least Common Multiple (LCM) of 140 and 170
The least common multiple (LCM) of 140 and 170 is 2380.
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 140 and 170?
First, calculate the GCD of 140 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 170 = 0 remainder 140 |
| 2 | 170 ÷ 140 = 1 remainder 30 |
| 3 | 140 ÷ 30 = 4 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 25 | 2275 |
| 99 and 151 | 14949 |
| 14 and 33 | 462 |
| 14 and 107 | 1498 |
| 108 and 110 | 5940 |