Least Common Multiple (LCM) of 68 and 21
The least common multiple (LCM) of 68 and 21 is 1428.
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 21?
First, calculate the GCD of 68 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 21 = 3 remainder 5 |
| 2 | 21 ÷ 5 = 4 remainder 1 |
| 3 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 42 | 588 |
| 21 and 130 | 2730 |
| 104 and 156 | 312 |
| 195 and 105 | 1365 |
| 76 and 139 | 10564 |