Least Common Multiple (LCM) of 116 and 70
The least common multiple (LCM) of 116 and 70 is 4060.
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 116 and 70?
First, calculate the GCD of 116 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 70 = 1 remainder 46 |
| 2 | 70 ÷ 46 = 1 remainder 24 |
| 3 | 46 ÷ 24 = 1 remainder 22 |
| 4 | 24 ÷ 22 = 1 remainder 2 |
| 5 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 69 | 12075 |
| 21 and 175 | 525 |
| 123 and 137 | 16851 |
| 181 and 51 | 9231 |
| 187 and 112 | 20944 |