Least Common Multiple (LCM) of 67 and 116
The least common multiple (LCM) of 67 and 116 is 7772.
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 116?
First, calculate the GCD of 67 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 116 = 0 remainder 67 |
| 2 | 116 ÷ 67 = 1 remainder 49 |
| 3 | 67 ÷ 49 = 1 remainder 18 |
| 4 | 49 ÷ 18 = 2 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 70 | 420 |
| 138 and 136 | 9384 |
| 111 and 56 | 6216 |
| 27 and 66 | 594 |
| 104 and 186 | 9672 |