Least Common Multiple (LCM) of 52 and 98
The least common multiple (LCM) of 52 and 98 is 2548.
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 98?
First, calculate the GCD of 52 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 98 = 0 remainder 52 |
| 2 | 98 ÷ 52 = 1 remainder 46 |
| 3 | 52 ÷ 46 = 1 remainder 6 |
| 4 | 46 ÷ 6 = 7 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 105 | 14070 |
| 107 and 49 | 5243 |
| 17 and 31 | 527 |
| 45 and 57 | 855 |
| 95 and 79 | 7505 |