Least Common Multiple (LCM) of 67 and 154
The least common multiple (LCM) of 67 and 154 is 10318.
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 154?
First, calculate the GCD of 67 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 154 = 0 remainder 67 |
| 2 | 154 ÷ 67 = 2 remainder 20 |
| 3 | 67 ÷ 20 = 3 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 20 | 540 |
| 99 and 162 | 1782 |
| 109 and 137 | 14933 |
| 62 and 118 | 3658 |
| 197 and 77 | 15169 |