Least Common Multiple (LCM) of 154 and 67
The least common multiple (LCM) of 154 and 67 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 154 and 67?
First, calculate the GCD of 154 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 67 = 2 remainder 20 |
| 2 | 67 ÷ 20 = 3 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 157 | 26219 |
| 61 and 144 | 8784 |
| 102 and 19 | 1938 |
| 127 and 34 | 4318 |
| 72 and 128 | 1152 |