Given Numbers are 345, 350

We can find the LCM of 345, 350 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 345 and 350

Multiples of 345 =345,690,1035,1380,1725,2070,2415,2760,3105,3450,3795,4140,4485,4830,5175,5520,5865,

Multiples of 350 =350,700,1050,1400,1750,2100,2450,2800,3150,3500,3850,4200,4550,4900,5250,5600,5950,

Now, get the least common multiple of 345, 350 which is 24150

So, the LCM of 345, 350 is 24150.

One method for determining the LCM of 345 and 350 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 345's prime factorization:

Prime factors of 345 are 3, 5,23.

345 = 3¹×5¹×23¹

And this is 350's prime factorization:

Prime factors of 350 are 2, 5,7.

350 = 2¹×5²×7¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3, 5,23, 2,7

2¹×3¹×5²×7¹×23¹ = 24150

This shows that the LCM of 345 and 350 is 24150.

The first step in determining the Least Common Multiple of 345 and 350 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 345 and 350:

Lets look at the first ten multiples of these numbers, 345 and 350:

345,690,1035,1380,1725,2070,2415,2760,3105,5865 are the first ten multiples of 345.

350,700,1050,1400,1750,2100,2450,2800,3150,5950 are the first ten multiples of 350.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 345 and 350, for example, are 4140, 5865, and 5600. 24150 is the least common multiple since it is the smallest.

345 and 350 have an LCM of 24150.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 350, than apply into the LCM equation.

GCF(345,350) = 5
LCM(345,350) = ( 345 × 350) / 5
LCM(345,350) = 120750 / 5
LCM(345,350) = 24150

1. What is the LCM of 345 and 350?

The LCM of 345 and 350 is 24150.

2. How to find the lowest common multiple of 345 and 350?

To find the lowest common multiple of 345 and 350, we have to get the multip;es of both numbers and identify the least common multiple in them which is 24150.

3. What are the Factors of 345?

Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.

4. What are the Factors of 350?

Answer: Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350. There are 12 integers that are factors of 350. The greatest factor of 350 is 350.

Answer:

Least Common Multiple of 345 and 350 = 24150

Step 1: Find the prime factorization of 345

345 = 3 x 5 x 23

Step 2: Find the prime factorization of 350

350 = 2 x 5 x 5 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 24150 = 2 x 3 x 5 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 345 and 350 is 24150.