Least Common Multiple (LCM) of 42 and 149
The least common multiple (LCM) of 42 and 149 is 6258.
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 42 and 149?
First, calculate the GCD of 42 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 149 = 0 remainder 42 |
| 2 | 149 ÷ 42 = 3 remainder 23 |
| 3 | 42 ÷ 23 = 1 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 113 | 21244 |
| 110 and 148 | 8140 |
| 126 and 54 | 378 |
| 153 and 162 | 2754 |
| 74 and 34 | 1258 |