Least Common Multiple (LCM) of 90 and 139
The least common multiple (LCM) of 90 and 139 is 12510.
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 139?
First, calculate the GCD of 90 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 139 = 0 remainder 90 |
| 2 | 139 ÷ 90 = 1 remainder 49 |
| 3 | 90 ÷ 49 = 1 remainder 41 |
| 4 | 49 ÷ 41 = 1 remainder 8 |
| 5 | 41 ÷ 8 = 5 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 121 | 21417 |
| 199 and 188 | 37412 |
| 133 and 180 | 23940 |
| 105 and 98 | 1470 |
| 46 and 151 | 6946 |