Least Common Multiple (LCM) of 52 and 89
The least common multiple (LCM) of 52 and 89 is 4628.
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 89?
First, calculate the GCD of 52 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 89 = 0 remainder 52 |
| 2 | 89 ÷ 52 = 1 remainder 37 |
| 3 | 52 ÷ 37 = 1 remainder 15 |
| 4 | 37 ÷ 15 = 2 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 199 | 14726 |
| 163 and 168 | 27384 |
| 179 and 105 | 18795 |
| 159 and 138 | 7314 |
| 116 and 120 | 3480 |