Least Common Multiple (LCM) of 53 and 194
The least common multiple (LCM) of 53 and 194 is 10282.
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 194?
First, calculate the GCD of 53 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 194 = 0 remainder 53 |
| 2 | 194 ÷ 53 = 3 remainder 35 |
| 3 | 53 ÷ 35 = 1 remainder 18 |
| 4 | 35 ÷ 18 = 1 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 123 | 2829 |
| 61 and 160 | 9760 |
| 99 and 30 | 990 |
| 130 and 15 | 390 |
| 88 and 125 | 11000 |