Least Common Multiple (LCM) of 115 and 70
The least common multiple (LCM) of 115 and 70 is 1610.
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 115 and 70?
First, calculate the GCD of 115 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 70 = 1 remainder 45 |
| 2 | 70 ÷ 45 = 1 remainder 25 |
| 3 | 45 ÷ 25 = 1 remainder 20 |
| 4 | 25 ÷ 20 = 1 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 198 | 33462 |
| 108 and 92 | 2484 |
| 137 and 154 | 21098 |
| 163 and 14 | 2282 |
| 172 and 19 | 3268 |