Least Common Multiple (LCM) of 87 and 150
The least common multiple (LCM) of 87 and 150 is 4350.
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 87 and 150?
First, calculate the GCD of 87 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 150 = 0 remainder 87 |
| 2 | 150 ÷ 87 = 1 remainder 63 |
| 3 | 87 ÷ 63 = 1 remainder 24 |
| 4 | 63 ÷ 24 = 2 remainder 15 |
| 5 | 24 ÷ 15 = 1 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 46 | 5014 |
| 14 and 55 | 770 |
| 165 and 93 | 5115 |
| 96 and 30 | 480 |
| 10 and 163 | 1630 |