Least Common Multiple (LCM) of 70 and 106
The least common multiple (LCM) of 70 and 106 is 3710.
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 106?
First, calculate the GCD of 70 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 106 = 0 remainder 70 |
| 2 | 106 ÷ 70 = 1 remainder 36 |
| 3 | 70 ÷ 36 = 1 remainder 34 |
| 4 | 36 ÷ 34 = 1 remainder 2 |
| 5 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 37 | 6882 |
| 65 and 168 | 10920 |
| 134 and 14 | 938 |
| 171 and 108 | 2052 |
| 124 and 100 | 3100 |