Least Common Multiple (LCM) of 72 and 78
The least common multiple (LCM) of 72 and 78 is 936.
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 72 and 78?
First, calculate the GCD of 72 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 78 = 0 remainder 72 |
| 2 | 78 ÷ 72 = 1 remainder 6 |
| 3 | 72 ÷ 6 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 86 | 9890 |
| 157 and 140 | 21980 |
| 105 and 117 | 4095 |
| 129 and 129 | 129 |
| 102 and 194 | 9894 |