Least Common Multiple (LCM) of 78 and 150
The least common multiple (LCM) of 78 and 150 is 1950.
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 78 and 150?
First, calculate the GCD of 78 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 150 = 0 remainder 78 |
| 2 | 150 ÷ 78 = 1 remainder 72 |
| 3 | 78 ÷ 72 = 1 remainder 6 |
| 4 | 72 ÷ 6 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 41 | 7462 |
| 163 and 41 | 6683 |
| 171 and 128 | 21888 |
| 175 and 100 | 700 |
| 175 and 160 | 5600 |