Least Common Multiple (LCM) of 107 and 67
The least common multiple (LCM) of 107 and 67 is 7169.
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 67?
First, calculate the GCD of 107 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 67 = 1 remainder 40 |
| 2 | 67 ÷ 40 = 1 remainder 27 |
| 3 | 40 ÷ 27 = 1 remainder 13 |
| 4 | 27 ÷ 13 = 2 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 31 | 2232 |
| 15 and 119 | 1785 |
| 161 and 79 | 12719 |
| 188 and 109 | 20492 |
| 191 and 32 | 6112 |