Least Common Multiple (LCM) of 90 and 149
The least common multiple (LCM) of 90 and 149 is 13410.
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 90 and 149?
First, calculate the GCD of 90 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 149 = 0 remainder 90 |
| 2 | 149 ÷ 90 = 1 remainder 59 |
| 3 | 90 ÷ 59 = 1 remainder 31 |
| 4 | 59 ÷ 31 = 1 remainder 28 |
| 5 | 31 ÷ 28 = 1 remainder 3 |
| 6 | 28 ÷ 3 = 9 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 35 | 70 |
| 42 and 152 | 3192 |
| 33 and 126 | 1386 |
| 59 and 45 | 2655 |
| 38 and 78 | 1482 |