Least Common Multiple (LCM) of 68 and 72
The least common multiple (LCM) of 68 and 72 is 1224.
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 68 and 72?
First, calculate the GCD of 68 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 72 = 0 remainder 68 |
| 2 | 72 ÷ 68 = 1 remainder 4 |
| 3 | 68 ÷ 4 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 89 | 6942 |
| 100 and 75 | 300 |
| 41 and 110 | 4510 |
| 112 and 49 | 784 |
| 111 and 171 | 6327 |