Least Common Multiple of 1981 and 1986

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

• Least Common Multiple of 1981 and 1986 by Prime method
• Least Common Multiple of 1981 and 1986 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 1981 and 1986. First we will calculate the prime factors of 1981 and 1986.

Prime Factorization of 1981

Prime factors of 1981 are 7,283. Prime factorization of 1981 in exponential form is:

1981 = 7¹×283¹

Prime Factorization of 1986

Prime factors of 1986 are 2, 3,331. Prime factorization of 1986 in exponential form is:

1986 = 2¹×3¹×331¹

Now multiplying the highest exponent prime factors to calculate the LCM of 1981 and 1986.

LCM(1981,1986) = 2¹×3¹×7¹×283¹×331¹
LCM(1981,1986) = 3934266

Factors of 1981

List of positive integer factors of 1981 that divides 1981 without a remainder.

1, 7, 283, 1981

Factors of 1986

List of positive integer factors of 1986 that divides 1986 without a remainder.

1, 2, 3, 6, 331, 662, 993, 1986

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1981 and 1986, than apply into the LCM equation.

GCF(1981,1986) = 1
LCM(1981,1986) = ( 1981 × 1986) / 1
LCM(1981,1986) = 3934266 / 1
LCM(1981,1986) = 3934266

(i) The LCM of 1986 and 1981 is associative

LCM of 1981 and 1986 = LCM of 1986 and 1981

1. What is the LCM of 1981 and 1986?

Answer: LCM of 1981 and 1986 is 3934266.

2. What are the Factors of 1981?

Answer: Factors of 1981 are 1, 7, 283, 1981. There are 4 integers that are factors of 1981. The greatest factor of 1981 is 1981.

3. What are the Factors of 1986?

Answer: Factors of 1986 are 1, 2, 3, 6, 331, 662, 993, 1986. There are 8 integers that are factors of 1986. The greatest factor of 1986 is 1986.

4. How to Find the LCM of 1981 and 1986?

Answer:

Least Common Multiple of 1981 and 1986 = 3934266

Step 1: Find the prime factorization of 1981

1981 = 7 x 283

Step 2: Find the prime factorization of 1986

1986 = 2 x 3 x 331

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

LCM = 3934266 = 2 x 3 x 7 x 283 x 331

Step 4: Therefore, the least common multiple of 1981 and 1986 is 3934266.