Least Common Multiple (LCM) of 67 and 76
The least common multiple (LCM) of 67 and 76 is 5092.
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 76?
First, calculate the GCD of 67 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 76 = 0 remainder 67 |
| 2 | 76 ÷ 67 = 1 remainder 9 |
| 3 | 67 ÷ 9 = 7 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 104 | 11128 |
| 108 and 146 | 7884 |
| 138 and 82 | 5658 |
| 55 and 52 | 2860 |
| 37 and 154 | 5698 |