Least Common Multiple (LCM) of 84 and 52
The least common multiple (LCM) of 84 and 52 is 1092.
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 52?
First, calculate the GCD of 84 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 52 = 1 remainder 32 |
| 2 | 52 ÷ 32 = 1 remainder 20 |
| 3 | 32 ÷ 20 = 1 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 11 | 1441 |
| 135 and 79 | 10665 |
| 141 and 135 | 6345 |
| 116 and 83 | 9628 |
| 57 and 19 | 57 |