Least Common Multiple of 1975 and 1982

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

• Least Common Multiple of 1975 and 1982 by Prime method
• Least Common Multiple of 1975 and 1982 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 1975 and 1982. First we will calculate the prime factors of 1975 and 1982.

Prime Factorization of 1975

Prime factors of 1975 are 5,79. Prime factorization of 1975 in exponential form is:

1975 = 5²×79¹

Prime Factorization of 1982

Prime factors of 1982 are 2,991. Prime factorization of 1982 in exponential form is:

1982 = 2¹×991¹

Now multiplying the highest exponent prime factors to calculate the LCM of 1975 and 1982.

LCM(1975,1982) = 2¹×5²×79¹×991¹
LCM(1975,1982) = 3914450

Factors of 1975

List of positive integer factors of 1975 that divides 1975 without a remainder.

1, 5, 25, 79, 395, 1975

Factors of 1982

List of positive integer factors of 1982 that divides 1982 without a remainder.

1, 2, 991, 1982

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1975 and 1982, than apply into the LCM equation.

GCF(1975,1982) = 1
LCM(1975,1982) = ( 1975 × 1982) / 1
LCM(1975,1982) = 3914450 / 1
LCM(1975,1982) = 3914450

(i) The LCM of 1982 and 1975 is associative

LCM of 1975 and 1982 = LCM of 1982 and 1975

1. What is the LCM of 1975 and 1982?

Answer: LCM of 1975 and 1982 is 3914450.

2. What are the Factors of 1975?

Answer: Factors of 1975 are 1, 5, 25, 79, 395, 1975. There are 6 integers that are factors of 1975. The greatest factor of 1975 is 1975.

3. What are the Factors of 1982?

Answer: Factors of 1982 are 1, 2, 991, 1982. There are 4 integers that are factors of 1982. The greatest factor of 1982 is 1982.

4. How to Find the LCM of 1975 and 1982?

Answer:

Least Common Multiple of 1975 and 1982 = 3914450

Step 1: Find the prime factorization of 1975

1975 = 5 x 5 x 79

Step 2: Find the prime factorization of 1982

1982 = 2 x 991

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

LCM = 3914450 = 2 x 5 x 5 x 79 x 991

Step 4: Therefore, the least common multiple of 1975 and 1982 is 3914450.