Least Common Multiple (LCM) of 52 and 84
The least common multiple (LCM) of 52 and 84 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 52 and 84?
First, calculate the GCD of 52 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 84 = 0 remainder 52 |
| 2 | 84 ÷ 52 = 1 remainder 32 |
| 3 | 52 ÷ 32 = 1 remainder 20 |
| 4 | 32 ÷ 20 = 1 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 76 | 1368 |
| 44 and 160 | 1760 |
| 139 and 192 | 26688 |
| 193 and 20 | 3860 |
| 180 and 28 | 1260 |