Least Common Multiple (LCM) of 108 and 67
The least common multiple (LCM) of 108 and 67 is 7236.
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 108 and 67?
First, calculate the GCD of 108 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 67 = 1 remainder 41 |
| 2 | 67 ÷ 41 = 1 remainder 26 |
| 3 | 41 ÷ 26 = 1 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 102 | 2958 |
| 129 and 61 | 7869 |
| 109 and 86 | 9374 |
| 135 and 184 | 24840 |
| 151 and 140 | 21140 |