Least Common Multiple (LCM) of 67 and 77
The least common multiple (LCM) of 67 and 77 is 5159.
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 77?
First, calculate the GCD of 67 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 77 = 0 remainder 67 |
| 2 | 77 ÷ 67 = 1 remainder 10 |
| 3 | 67 ÷ 10 = 6 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 88 | 7656 |
| 148 and 119 | 17612 |
| 81 and 10 | 810 |
| 162 and 53 | 8586 |
| 166 and 129 | 21414 |