Least Common Multiple (LCM) of 53 and 191
The least common multiple (LCM) of 53 and 191 is 10123.
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 191?
First, calculate the GCD of 53 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 191 = 0 remainder 53 |
| 2 | 191 ÷ 53 = 3 remainder 32 |
| 3 | 53 ÷ 32 = 1 remainder 21 |
| 4 | 32 ÷ 21 = 1 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 100 | 12300 |
| 76 and 178 | 6764 |
| 73 and 68 | 4964 |
| 76 and 136 | 2584 |
| 75 and 172 | 12900 |