Least Common Multiple of 1981 and 1988

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

• Least Common Multiple of 1981 and 1988 by Prime method
• Least Common Multiple of 1981 and 1988 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 1981 and 1988. First we will calculate the prime factors of 1981 and 1988.

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 1988

Prime factors of 1988 are 2, 7,71. Prime factorization of 1988 in exponential form is:

1988 = 2²×7¹×71¹

Now multiplying the highest exponent prime factors to calculate the LCM of 1981 and 1988.

LCM(1981,1988) = 2²×7¹×71¹×283¹
LCM(1981,1988) = 562604

Factors of 1981

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

1, 7, 283, 1981

Factors of 1988

List of positive integer factors of 1988 that divides 1988 without a remainder.

1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, 1988

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1981 and 1988, than apply into the LCM equation.

GCF(1981,1988) = 7
LCM(1981,1988) = ( 1981 × 1988) / 7
LCM(1981,1988) = 3938228 / 7
LCM(1981,1988) = 562604

(i) The LCM of 1988 and 1981 is associative

LCM of 1981 and 1988 = LCM of 1988 and 1981

1. What is the LCM of 1981 and 1988?

Answer: LCM of 1981 and 1988 is 562604.

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 1988?

Answer: Factors of 1988 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 497, 994, 1988. There are 12 integers that are factors of 1988. The greatest factor of 1988 is 1988.

4. How to Find the LCM of 1981 and 1988?

Answer:

Least Common Multiple of 1981 and 1988 = 562604

Step 1: Find the prime factorization of 1981

1981 = 7 x 283

Step 2: Find the prime factorization of 1988

1988 = 2 x 2 x 7 x 71

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

LCM = 562604 = 2 x 2 x 7 x 71 x 283

Step 4: Therefore, the least common multiple of 1981 and 1988 is 562604.