Least Common Multiple (LCM) of 53 and 190
The least common multiple (LCM) of 53 and 190 is 10070.
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 190?
First, calculate the GCD of 53 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 190 = 0 remainder 53 |
| 2 | 190 ÷ 53 = 3 remainder 31 |
| 3 | 53 ÷ 31 = 1 remainder 22 |
| 4 | 31 ÷ 22 = 1 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 132 | 8052 |
| 162 and 62 | 5022 |
| 189 and 74 | 13986 |
| 144 and 106 | 7632 |
| 115 and 194 | 22310 |