Least Common Multiple (LCM) of 145 and 78
The least common multiple (LCM) of 145 and 78 is 11310.
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 145 and 78?
First, calculate the GCD of 145 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 78 = 1 remainder 67 |
| 2 | 78 ÷ 67 = 1 remainder 11 |
| 3 | 67 ÷ 11 = 6 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 200 | 1400 |
| 84 and 174 | 2436 |
| 14 and 49 | 98 |
| 40 and 106 | 2120 |
| 143 and 68 | 9724 |