Least Common Multiple (LCM) of 100 and 174
The least common multiple (LCM) of 100 and 174 is 8700.
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 100 and 174?
First, calculate the GCD of 100 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 174 = 0 remainder 100 |
| 2 | 174 ÷ 100 = 1 remainder 74 |
| 3 | 100 ÷ 74 = 1 remainder 26 |
| 4 | 74 ÷ 26 = 2 remainder 22 |
| 5 | 26 ÷ 22 = 1 remainder 4 |
| 6 | 22 ÷ 4 = 5 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 109 | 11227 |
| 54 and 44 | 1188 |
| 16 and 102 | 816 |
| 102 and 45 | 1530 |
| 121 and 63 | 7623 |