Least Common Multiple of 10067 and 10074

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

• Least Common Multiple of 10067 and 10074 by Prime method
• Least Common Multiple of 10067 and 10074 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10067 and 10074. First we will calculate the prime factors of 10067 and 10074.

Prime Factorization of 10067

Prime factors of 10067 are 10067. Prime factorization of 10067 in exponential form is:

10067 = 10067¹

Prime Factorization of 10074

Prime factors of 10074 are 2, 3, 23,73. Prime factorization of 10074 in exponential form is:

10074 = 2¹×3¹×23¹×73¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10067 and 10074.

LCM(10067,10074) = 2¹×3¹×23¹×73¹×10067¹
LCM(10067,10074) = 101414958

Factors of 10067

List of positive integer factors of 10067 that divides 10067 without a remainder.

1, 10067

Factors of 10074

List of positive integer factors of 10074 that divides 10074 without a remainder.

1, 2, 3, 6, 23, 46, 69, 73, 138, 146, 219, 438, 1679, 3358, 5037, 10074

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10067 and 10074, than apply into the LCM equation.

GCF(10067,10074) = 1
LCM(10067,10074) = ( 10067 × 10074) / 1
LCM(10067,10074) = 101414958 / 1
LCM(10067,10074) = 101414958

(i) The LCM of 10074 and 10067 is associative

LCM of 10067 and 10074 = LCM of 10074 and 10067

1. What is the LCM of 10067 and 10074?

Answer: LCM of 10067 and 10074 is 101414958.

2. What are the Factors of 10067?

Answer: Factors of 10067 are 1, 10067. There are 2 integers that are factors of 10067. The greatest factor of 10067 is 10067.

3. What are the Factors of 10074?

Answer: Factors of 10074 are 1, 2, 3, 6, 23, 46, 69, 73, 138, 146, 219, 438, 1679, 3358, 5037, 10074. There are 16 integers that are factors of 10074. The greatest factor of 10074 is 10074.

4. How to Find the LCM of 10067 and 10074?

Answer:

Least Common Multiple of 10067 and 10074 = 101414958

Step 1: Find the prime factorization of 10067

10067 = 10067

Step 2: Find the prime factorization of 10074

10074 = 2 x 3 x 23 x 73

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

LCM = 101414958 = 2 x 3 x 23 x 73 x 10067

Step 4: Therefore, the least common multiple of 10067 and 10074 is 101414958.