Least Common Multiple (LCM) of 189 and 52
The least common multiple (LCM) of 189 and 52 is 9828.
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 189 and 52?
First, calculate the GCD of 189 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 52 = 3 remainder 33 |
| 2 | 52 ÷ 33 = 1 remainder 19 |
| 3 | 33 ÷ 19 = 1 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 120 | 3960 |
| 197 and 60 | 11820 |
| 54 and 186 | 1674 |
| 48 and 166 | 3984 |
| 52 and 77 | 4004 |