Least Common Multiple (LCM) of 67 and 21
The least common multiple (LCM) of 67 and 21 is 1407.
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 21?
First, calculate the GCD of 67 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 21 = 3 remainder 4 |
| 2 | 21 ÷ 4 = 5 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 50 | 2600 |
| 109 and 138 | 15042 |
| 66 and 43 | 2838 |
| 181 and 43 | 7783 |
| 146 and 188 | 13724 |