Least Common Multiple (LCM) of 108 and 70
The least common multiple (LCM) of 108 and 70 is 3780.
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 108 and 70?
First, calculate the GCD of 108 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 70 = 1 remainder 38 |
| 2 | 70 ÷ 38 = 1 remainder 32 |
| 3 | 38 ÷ 32 = 1 remainder 6 |
| 4 | 32 ÷ 6 = 5 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 123 | 7257 |
| 51 and 121 | 6171 |
| 122 and 144 | 8784 |
| 197 and 138 | 27186 |
| 80 and 100 | 400 |