Least Common Multiple (LCM) of 106 and 70
The least common multiple (LCM) of 106 and 70 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 106 and 70?
First, calculate the GCD of 106 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 70 = 1 remainder 36 |
| 2 | 70 ÷ 36 = 1 remainder 34 |
| 3 | 36 ÷ 34 = 1 remainder 2 |
| 4 | 34 ÷ 2 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 15 | 1815 |
| 130 and 105 | 2730 |
| 167 and 126 | 21042 |
| 49 and 37 | 1813 |
| 40 and 78 | 1560 |