Least Common Multiple (LCM) of 107 and 156
The least common multiple (LCM) of 107 and 156 is 16692.
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 107 and 156?
First, calculate the GCD of 107 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 156 = 0 remainder 107 |
| 2 | 156 ÷ 107 = 1 remainder 49 |
| 3 | 107 ÷ 49 = 2 remainder 9 |
| 4 | 49 ÷ 9 = 5 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 38 | 1178 |
| 74 and 109 | 8066 |
| 60 and 110 | 660 |
| 80 and 20 | 80 |
| 149 and 28 | 4172 |