Least Common Multiple (LCM) of 67 and 88
The least common multiple (LCM) of 67 and 88 is 5896.
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 88?
First, calculate the GCD of 67 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 88 = 0 remainder 67 |
| 2 | 88 ÷ 67 = 1 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 |
|---|---|
| 24 and 115 | 2760 |
| 15 and 128 | 1920 |
| 40 and 177 | 7080 |
| 107 and 119 | 12733 |
| 80 and 30 | 240 |