Least Common Multiple of 458 and 465

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 458 and 465 the smallest integer that is 212970 that is divisible by both numbers.

Least Common Multiple (LCM) of 458 and 465 is 212970.

LCM(458,465) = 212970

LCM of 458 and 465

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

LCM of:
and

Least Common Multiple of 458 and 465

LCM of 458 and 465 is 212970

Least common multiple can be found by multiplying the highest exponent prime factors of 458 and 465. First we will calculate the prime factors of 458 and 465.

Prime Factorization of 458


2 458
229 229
1

Prime factors of 458 are 2,229. Prime factorization of 458 in exponential form is:

458 = 21×2291

Prime Factorization of 465


3 465
5 155
31 31
1

Prime factors of 465 are 3, 5,31. Prime factorization of 465 in exponential form is:

465 = 31×51×311

Now multiplying the highest exponent prime factors to calculate the LCM of 458 and 465.

LCM(458,465) = 21×31×51×311×2291
LCM(458,465) = 212970

Factors of 458

List of positive integer factors of 458 that divides 458 without a remainder.

1, 2, 229, 458

Factors of 465

List of positive integer factors of 465 that divides 465 without a remainder.

1, 3, 5, 15, 31, 93, 155, 465

Least Common Multiple of 458 and 465 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 458 and 465, than apply into the LCM equation.

GCF(458,465) = 1
LCM(458,465) = ( 458 × 465) / 1
LCM(458,465) = 212970 / 1
LCM(458,465) = 212970

Properties of LCM 458 and 465

(i) The LCM of 465 and 458 is associative

LCM of 458 and 465 = LCM of 465 and 458

Related Least Common Multiples of 458

Related Least Common Multiples of 465

Frequently Asked Questions on LCM of 458 and 465

1. What is the LCM of 458 and 465?

Answer: LCM of 458 and 465 is 212970.

2. What are the Factors of 458?

Answer: Factors of 458 are 1, 2, 229, 458. There are 4 integers that are factors of 458. The greatest factor of 458 is 458.

3. What are the Factors of 465?

Answer: Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. There are 8 integers that are factors of 465. The greatest factor of 465 is 465.

4. How to Find the LCM of 458 and 465?

Answer:

Least Common Multiple of 458 and 465 = 212970

Step 1: Find the prime factorization of 458

458 = 2 x 229

Step 2: Find the prime factorization of 465

465 = 3 x 5 x 31

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

LCM = 212970 = 2 x 3 x 5 x 31 x 229

Step 4: Therefore, the least common multiple of 458 and 465 is 212970.