Least Common Multiple (LCM) of 45 and 148
The least common multiple (LCM) of 45 and 148 is 6660.
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 45 and 148?
First, calculate the GCD of 45 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 148 = 0 remainder 45 |
| 2 | 148 ÷ 45 = 3 remainder 13 |
| 3 | 45 ÷ 13 = 3 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 174 | 11310 |
| 140 and 182 | 1820 |
| 177 and 119 | 21063 |
| 115 and 184 | 920 |
| 71 and 189 | 13419 |