Least Common Multiple of 1967 and 1974

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

• Least Common Multiple of 1967 and 1974 by Prime method
• Least Common Multiple of 1967 and 1974 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 1967 and 1974. First we will calculate the prime factors of 1967 and 1974.

Prime Factorization of 1967

Prime factors of 1967 are 7,281. Prime factorization of 1967 in exponential form is:

1967 = 7¹×281¹

Prime Factorization of 1974

Prime factors of 1974 are 2, 3, 7,47. Prime factorization of 1974 in exponential form is:

1974 = 2¹×3¹×7¹×47¹

Now multiplying the highest exponent prime factors to calculate the LCM of 1967 and 1974.

LCM(1967,1974) = 2¹×3¹×7¹×47¹×281¹
LCM(1967,1974) = 554694

Factors of 1967

List of positive integer factors of 1967 that divides 1967 without a remainder.

1, 7, 281, 1967

Factors of 1974

List of positive integer factors of 1974 that divides 1974 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1967 and 1974, than apply into the LCM equation.

GCF(1967,1974) = 7
LCM(1967,1974) = ( 1967 × 1974) / 7
LCM(1967,1974) = 3882858 / 7
LCM(1967,1974) = 554694

(i) The LCM of 1974 and 1967 is associative

LCM of 1967 and 1974 = LCM of 1974 and 1967

1. What is the LCM of 1967 and 1974?

Answer: LCM of 1967 and 1974 is 554694.

2. What are the Factors of 1967?

Answer: Factors of 1967 are 1, 7, 281, 1967. There are 4 integers that are factors of 1967. The greatest factor of 1967 is 1967.

3. What are the Factors of 1974?

Answer: Factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974. There are 16 integers that are factors of 1974. The greatest factor of 1974 is 1974.

4. How to Find the LCM of 1967 and 1974?

Answer:

Least Common Multiple of 1967 and 1974 = 554694

Step 1: Find the prime factorization of 1967

1967 = 7 x 281

Step 2: Find the prime factorization of 1974

1974 = 2 x 3 x 7 x 47

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

LCM = 554694 = 2 x 3 x 7 x 47 x 281

Step 4: Therefore, the least common multiple of 1967 and 1974 is 554694.