Least Common Multiple (LCM) of 53 and 19
The least common multiple (LCM) of 53 and 19 is 1007.
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 19?
First, calculate the GCD of 53 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 19 = 2 remainder 15 |
| 2 | 19 ÷ 15 = 1 remainder 4 |
| 3 | 15 ÷ 4 = 3 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 89 | 10502 |
| 178 and 81 | 14418 |
| 90 and 164 | 7380 |
| 84 and 115 | 9660 |
| 51 and 20 | 1020 |