Least Common Multiple (LCM) of 19 and 148
The least common multiple (LCM) of 19 and 148 is 2812.
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 19 and 148?
First, calculate the GCD of 19 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 148 = 0 remainder 19 |
| 2 | 148 ÷ 19 = 7 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 167 | 15531 |
| 105 and 152 | 15960 |
| 174 and 89 | 15486 |
| 184 and 185 | 34040 |
| 165 and 166 | 27390 |