Least Common Multiple (LCM) of 194 and 53
The least common multiple (LCM) of 194 and 53 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 194 and 53?
First, calculate the GCD of 194 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 53 = 3 remainder 35 |
| 2 | 53 ÷ 35 = 1 remainder 18 |
| 3 | 35 ÷ 18 = 1 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 71 | 9869 |
| 135 and 137 | 18495 |
| 68 and 196 | 3332 |
| 194 and 180 | 17460 |
| 84 and 111 | 3108 |