Least Common Multiple (LCM) of 53 and 84
The least common multiple (LCM) of 53 and 84 is 4452.
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 53 and 84?
First, calculate the GCD of 53 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 84 = 0 remainder 53 |
| 2 | 84 ÷ 53 = 1 remainder 31 |
| 3 | 53 ÷ 31 = 1 remainder 22 |
| 4 | 31 ÷ 22 = 1 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 15 | 855 |
| 105 and 112 | 1680 |
| 61 and 85 | 5185 |
| 161 and 124 | 19964 |
| 126 and 178 | 11214 |