Least Common Multiple (LCM) of 78 and 148
The least common multiple (LCM) of 78 and 148 is 5772.
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 148?
First, calculate the GCD of 78 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 148 = 0 remainder 78 |
| 2 | 148 ÷ 78 = 1 remainder 70 |
| 3 | 78 ÷ 70 = 1 remainder 8 |
| 4 | 70 ÷ 8 = 8 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 72 | 1440 |
| 105 and 176 | 18480 |
| 50 and 23 | 1150 |
| 163 and 23 | 3749 |
| 112 and 53 | 5936 |