Least Common Multiple (LCM) of 148 and 53
The least common multiple (LCM) of 148 and 53 is 7844.
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 148 and 53?
First, calculate the GCD of 148 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 148 ÷ 53 = 2 remainder 42 |
| 2 | 53 ÷ 42 = 1 remainder 11 |
| 3 | 42 ÷ 11 = 3 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 59 | 3422 |
| 84 and 164 | 3444 |
| 46 and 169 | 7774 |
| 186 and 194 | 18042 |
| 147 and 109 | 16023 |