Least Common Multiple of 7998 and 8005

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 7998 and 8005 by Prime method
• Least Common Multiple of 7998 and 8005 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7998 and 8005. First we will calculate the prime factors of 7998 and 8005.

Prime Factorization of 7998

Prime factors of 7998 are 2, 3, 31,43. Prime factorization of 7998 in exponential form is:

7998 = 2¹×3¹×31¹×43¹

Prime Factorization of 8005

Prime factors of 8005 are 5,1601. Prime factorization of 8005 in exponential form is:

8005 = 5¹×1601¹

Now multiplying the highest exponent prime factors to calculate the LCM of 7998 and 8005.

LCM(7998,8005) = 2¹×3¹×5¹×31¹×43¹×1601¹
LCM(7998,8005) = 64023990

Factors of 7998

List of positive integer factors of 7998 that divides 7998 without a remainder.

1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998

Factors of 8005

List of positive integer factors of 8005 that divides 8005 without a remainder.

1, 5, 1601, 8005

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7998 and 8005, than apply into the LCM equation.

GCF(7998,8005) = 1
LCM(7998,8005) = ( 7998 × 8005) / 1
LCM(7998,8005) = 64023990 / 1
LCM(7998,8005) = 64023990

(i) The LCM of 8005 and 7998 is associative

LCM of 7998 and 8005 = LCM of 8005 and 7998

1. What is the LCM of 7998 and 8005?

Answer: LCM of 7998 and 8005 is 64023990.

2. What are the Factors of 7998?

Answer: Factors of 7998 are 1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998. There are 16 integers that are factors of 7998. The greatest factor of 7998 is 7998.

3. What are the Factors of 8005?

Answer: Factors of 8005 are 1, 5, 1601, 8005. There are 4 integers that are factors of 8005. The greatest factor of 8005 is 8005.

4. How to Find the LCM of 7998 and 8005?

Answer:

Least Common Multiple of 7998 and 8005 = 64023990

Step 1: Find the prime factorization of 7998

7998 = 2 x 3 x 31 x 43

Step 2: Find the prime factorization of 8005

8005 = 5 x 1601

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

LCM = 64023990 = 2 x 3 x 5 x 31 x 43 x 1601

Step 4: Therefore, the least common multiple of 7998 and 8005 is 64023990.