Least Common Multiple (LCM) of 117 and 70
The least common multiple (LCM) of 117 and 70 is 8190.
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 117 and 70?
First, calculate the GCD of 117 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 70 = 1 remainder 47 |
| 2 | 70 ÷ 47 = 1 remainder 23 |
| 3 | 47 ÷ 23 = 2 remainder 1 |
| 4 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 50 | 150 |
| 49 and 134 | 6566 |
| 138 and 135 | 6210 |
| 129 and 31 | 3999 |
| 29 and 27 | 783 |