1,325 is not a prime number but a composite one.

116 is not a prime number but a composite one.

* A composite number is a natural number that has at least one other factor than 1 and itself.

lcm (1,325; 116) = 2

1,325 ÷ 116 = 11 + 49

Step 2. Divide the smaller number by the above operation's remainder:

116 ÷ 49 = 2 + 18

Step 3. Divide the remainder of the step 1 by the remainder of the step 2:

49 ÷ 18 = 2 + 13

Step 4. Divide the remainder of the step 2 by the remainder of the step 3:

18 ÷ 13 = 1 + 5

Step 5. Divide the remainder of the step 3 by the remainder of the step 4:

13 ÷ 5 = 2 + 3

Step 6. Divide the remainder of the step 4 by the remainder of the step 5:

5 ÷ 3 = 1 + 2

Step 7. Divide the remainder of the step 5 by the remainder of the step 6:

3 ÷ 2 = 1 + 1

Step 8. Divide the remainder of the step 6 by the remainder of the step 7:

2 ÷ 1 = 2 + 0

At this step, the remainder is zero, so we stop:

1 is the number we were looking for - the last non-zero remainder.

This is the greatest (highest) common factor (divisor).

gcf, hcf, gcd (1,325; 116) = 1

lcm (1,325; 116) = 153,700 = 2

The two numbers have no prime factors in common:

153,700 = 1,325 × 116

lcm (a; b) =

- The number 60 is a common multiple of the numbers 6 and 15 because 60 is a multiple of 6 (60 = 6 × 10) and also a multiple of 15 (60 = 15 × 4).
**There are infinitely many common multiples of 6 and 15.**

**If the number "v" is a multiple of the numbers "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".**- The common multiples of 6 and 15 are the numbers 30, 60, 90, 120, and so on.
- Out of these, 30 is the smallest, 30 is the least common multiple (lcm) of 6 and 15.

- Note: The
**prime factorization**of a number: finding the prime numbers that multiply together to give that number. **If e = lcm (a, b), then the prime factorization of "e" must contain all the prime factors involved in the prime factorization of "a" and "b" taken by the highest power.**

**Example:**- 40 = 2
^{3}× 5 - 36 = 2
^{2}× 3^{2} - 126 = 2 × 3
^{2}× 7 - lcm (40, 36, 126) = 2
^{3}× 3^{2}× 5 × 7 = 2,520 **Note:**2^{3}= 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. Or, shorter, 2 to the power of 3. In this example 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 2^{3}is the power and 8 is the value of the power:

**Another example of calculating the least common multiple, lcm:**- 938 = 2 × 7 × 67
- 982 = 2 × 491
- 743 = is a prime number and cannot be broken down into other prime factors
- lcm (938, 982, 743) = 2 × 7 × 67 × 491 × 743 = 342,194,594

**If two or more numbers have no common factors (they are coprime)**, then their least common multiple is calculated by simply multiplying the numbers.- Example:
- 6 = 2 × 3
- 35 = 5 × 7
- lcm (6, 35) = 2 × 3 × 5 × 7 = 6 × 35 = 210