Least Common Multiple (LCM) of 67 and 18
The least common multiple (LCM) of 67 and 18 is 1206.
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 18?
First, calculate the GCD of 67 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 18 = 3 remainder 13 |
| 2 | 18 ÷ 13 = 1 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 82 | 13694 |
| 171 and 137 | 23427 |
| 138 and 25 | 3450 |
| 56 and 86 | 2408 |
| 32 and 161 | 5152 |