Least Common Multiple (LCM) of 70 and 117
The least common multiple (LCM) of 70 and 117 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 70 and 117?
First, calculate the GCD of 70 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 117 = 0 remainder 70 |
| 2 | 117 ÷ 70 = 1 remainder 47 |
| 3 | 70 ÷ 47 = 1 remainder 23 |
| 4 | 47 ÷ 23 = 2 remainder 1 |
| 5 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 54 | 2538 |
| 77 and 139 | 10703 |
| 151 and 137 | 20687 |
| 89 and 157 | 13973 |
| 156 and 126 | 3276 |