Least Common Multiple (LCM) of 147 and 78
The least common multiple (LCM) of 147 and 78 is 3822.
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 147 and 78?
First, calculate the GCD of 147 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 78 = 1 remainder 69 |
| 2 | 78 ÷ 69 = 1 remainder 9 |
| 3 | 69 ÷ 9 = 7 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 99 | 11484 |
| 93 and 39 | 1209 |
| 156 and 163 | 25428 |
| 76 and 188 | 3572 |
| 54 and 110 | 2970 |