Least Common Multiple (LCM) of 67 and 187
The least common multiple (LCM) of 67 and 187 is 12529.
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 67 and 187?
First, calculate the GCD of 67 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 187 = 0 remainder 67 |
| 2 | 187 ÷ 67 = 2 remainder 53 |
| 3 | 67 ÷ 53 = 1 remainder 14 |
| 4 | 53 ÷ 14 = 3 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 193 | 25476 |
| 24 and 115 | 2760 |
| 15 and 49 | 735 |
| 152 and 177 | 26904 |
| 41 and 101 | 4141 |