Least Common Multiple (LCM) of 67 and 155
The least common multiple (LCM) of 67 and 155 is 10385.
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 155?
First, calculate the GCD of 67 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 155 = 0 remainder 67 |
| 2 | 155 ÷ 67 = 2 remainder 21 |
| 3 | 67 ÷ 21 = 3 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 74 | 1110 |
| 115 and 149 | 17135 |
| 97 and 133 | 12901 |
| 117 and 119 | 13923 |
| 64 and 196 | 3136 |