Least Common Multiple (LCM) of 84 and 73
The least common multiple (LCM) of 84 and 73 is 6132.
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 84 and 73?
First, calculate the GCD of 84 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 73 = 1 remainder 11 |
| 2 | 73 ÷ 11 = 6 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 74 | 1110 |
| 29 and 19 | 551 |
| 142 and 86 | 6106 |
| 53 and 70 | 3710 |
| 103 and 77 | 7931 |