Least Common Multiple (LCM) of 90 and 151
The least common multiple (LCM) of 90 and 151 is 13590.
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 151?
First, calculate the GCD of 90 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 151 = 0 remainder 90 |
| 2 | 151 ÷ 90 = 1 remainder 61 |
| 3 | 90 ÷ 61 = 1 remainder 29 |
| 4 | 61 ÷ 29 = 2 remainder 3 |
| 5 | 29 ÷ 3 = 9 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 88 | 10120 |
| 42 and 165 | 2310 |
| 50 and 119 | 5950 |
| 108 and 155 | 16740 |
| 27 and 89 | 2403 |