Least Common Multiple (LCM) of 67 and 19
The least common multiple (LCM) of 67 and 19 is 1273.
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 67 and 19?
First, calculate the GCD of 67 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 19 = 3 remainder 10 |
| 2 | 19 ÷ 10 = 1 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 14 | 714 |
| 71 and 176 | 12496 |
| 149 and 186 | 27714 |
| 195 and 75 | 975 |
| 123 and 170 | 20910 |