Least Common Multiple (LCM) of 67 and 84
The least common multiple (LCM) of 67 and 84 is 5628.
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 84?
First, calculate the GCD of 67 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 84 = 0 remainder 67 |
| 2 | 84 ÷ 67 = 1 remainder 17 |
| 3 | 67 ÷ 17 = 3 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 22 | 1518 |
| 172 and 42 | 3612 |
| 73 and 110 | 8030 |
| 117 and 168 | 6552 |
| 54 and 68 | 1836 |