Least Common Multiple (LCM) of 101 and 149
The least common multiple (LCM) of 101 and 149 is 15049.
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 101 and 149?
First, calculate the GCD of 101 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 149 = 0 remainder 101 |
| 2 | 149 ÷ 101 = 1 remainder 48 |
| 3 | 101 ÷ 48 = 2 remainder 5 |
| 4 | 48 ÷ 5 = 9 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 113 | 11639 |
| 129 and 64 | 8256 |
| 191 and 161 | 30751 |
| 58 and 57 | 3306 |
| 181 and 30 | 5430 |