Least Common Multiple (LCM) of 67 and 79
The least common multiple (LCM) of 67 and 79 is 5293.
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 79?
First, calculate the GCD of 67 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 79 = 0 remainder 67 |
| 2 | 79 ÷ 67 = 1 remainder 12 |
| 3 | 67 ÷ 12 = 5 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 185 | 740 |
| 152 and 72 | 1368 |
| 178 and 110 | 9790 |
| 91 and 49 | 637 |
| 183 and 42 | 2562 |