Least Common Multiple (LCM) of 74 and 101
The least common multiple (LCM) of 74 and 101 is 7474.
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 74 and 101?
First, calculate the GCD of 74 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 101 = 0 remainder 74 |
| 2 | 101 ÷ 74 = 1 remainder 27 |
| 3 | 74 ÷ 27 = 2 remainder 20 |
| 4 | 27 ÷ 20 = 1 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 52 | 3692 |
| 165 and 128 | 21120 |
| 139 and 195 | 27105 |
| 93 and 200 | 18600 |
| 61 and 170 | 10370 |