Least Common Multiple of 1464 and 1470

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1464 and 1470 the smallest integer that is 358680 that is divisible by both numbers.

Least Common Multiple (LCM) of 1464 and 1470 is 358680.

LCM(1464,1470) = 358680

LCM of 1464 and 1470

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

LCM of:
and

Least Common Multiple of 1464 and 1470

LCM of 1464 and 1470 is 358680

Least common multiple can be found by multiplying the highest exponent prime factors of 1464 and 1470. First we will calculate the prime factors of 1464 and 1470.

Prime Factorization of 1464


2 1464
2 732
2 366
3 183
61 61
1

Prime factors of 1464 are 2, 3,61. Prime factorization of 1464 in exponential form is:

1464 = 23×31×611

Prime Factorization of 1470


2 1470
3 735
5 245
7 49
7 7
1

Prime factors of 1470 are 2, 3, 5,7. Prime factorization of 1470 in exponential form is:

1470 = 21×31×51×72

Now multiplying the highest exponent prime factors to calculate the LCM of 1464 and 1470.

LCM(1464,1470) = 23×31×51×72×611
LCM(1464,1470) = 358680

Factors of 1464

List of positive integer factors of 1464 that divides 1464 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464

Factors of 1470

List of positive integer factors of 1470 that divides 1470 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470

Least Common Multiple of 1464 and 1470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1464 and 1470, than apply into the LCM equation.

GCF(1464,1470) = 6
LCM(1464,1470) = ( 1464 × 1470) / 6
LCM(1464,1470) = 2152080 / 6
LCM(1464,1470) = 358680

Properties of LCM 1464 and 1470

(i) The LCM of 1470 and 1464 is associative

LCM of 1464 and 1470 = LCM of 1470 and 1464

Related Least Common Multiples of 1464

Related Least Common Multiples of 1470

Frequently Asked Questions on LCM of 1464 and 1470

1. What is the LCM of 1464 and 1470?

Answer: LCM of 1464 and 1470 is 358680.

2. What are the Factors of 1464?

Answer: Factors of 1464 are 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464. There are 16 integers that are factors of 1464. The greatest factor of 1464 is 1464.

3. What are the Factors of 1470?

Answer: Factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470. There are 24 integers that are factors of 1470. The greatest factor of 1470 is 1470.

4. How to Find the LCM of 1464 and 1470?

Answer:

Least Common Multiple of 1464 and 1470 = 358680

Step 1: Find the prime factorization of 1464

1464 = 2 x 2 x 2 x 3 x 61

Step 2: Find the prime factorization of 1470

1470 = 2 x 3 x 5 x 7 x 7

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

LCM = 358680 = 2 x 2 x 2 x 3 x 5 x 7 x 7 x 61

Step 4: Therefore, the least common multiple of 1464 and 1470 is 358680.