Least Common Multiple (LCM) of 53 and 98
The least common multiple (LCM) of 53 and 98 is 5194.
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 98?
First, calculate the GCD of 53 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 98 = 0 remainder 53 |
| 2 | 98 ÷ 53 = 1 remainder 45 |
| 3 | 53 ÷ 45 = 1 remainder 8 |
| 4 | 45 ÷ 8 = 5 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 98 | 196 |
| 10 and 79 | 790 |
| 38 and 194 | 3686 |
| 172 and 100 | 4300 |
| 102 and 172 | 8772 |