Least Common Multiple (LCM) of 190 and 53
The least common multiple (LCM) of 190 and 53 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 190 and 53?
First, calculate the GCD of 190 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 53 = 3 remainder 31 |
| 2 | 53 ÷ 31 = 1 remainder 22 |
| 3 | 31 ÷ 22 = 1 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 134 | 19698 |
| 14 and 107 | 1498 |
| 167 and 33 | 5511 |
| 200 and 167 | 33400 |
| 120 and 151 | 18120 |