Least Common Multiple (LCM) of 107 and 70
The least common multiple (LCM) of 107 and 70 is 7490.
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 107 and 70?
First, calculate the GCD of 107 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 70 = 1 remainder 37 |
| 2 | 70 ÷ 37 = 1 remainder 33 |
| 3 | 37 ÷ 33 = 1 remainder 4 |
| 4 | 33 ÷ 4 = 8 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 126 | 8568 |
| 139 and 76 | 10564 |
| 178 and 180 | 16020 |
| 16 and 159 | 2544 |
| 189 and 50 | 9450 |