Least Common Multiple (LCM) of 60 and 19
The least common multiple (LCM) of 60 and 19 is 1140.
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 60 and 19?
First, calculate the GCD of 60 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 19 = 3 remainder 3 |
| 2 | 19 ÷ 3 = 6 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 32 | 1440 |
| 138 and 130 | 8970 |
| 135 and 143 | 19305 |
| 29 and 96 | 2784 |
| 182 and 199 | 36218 |