Least Common Multiple (LCM) of 102 and 149
The least common multiple (LCM) of 102 and 149 is 15198.
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 102 and 149?
First, calculate the GCD of 102 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 149 = 0 remainder 102 |
| 2 | 149 ÷ 102 = 1 remainder 47 |
| 3 | 102 ÷ 47 = 2 remainder 8 |
| 4 | 47 ÷ 8 = 5 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 166 | 9628 |
| 72 and 148 | 2664 |
| 180 and 35 | 1260 |
| 193 and 108 | 20844 |
| 123 and 81 | 3321 |