Least Common Multiple (LCM) of 72 and 106
The least common multiple (LCM) of 72 and 106 is 3816.
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 72 and 106?
First, calculate the GCD of 72 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 106 = 0 remainder 72 |
| 2 | 106 ÷ 72 = 1 remainder 34 |
| 3 | 72 ÷ 34 = 2 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 52 | 8372 |
| 85 and 130 | 2210 |
| 168 and 134 | 11256 |
| 138 and 163 | 22494 |
| 189 and 18 | 378 |