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118 LearnersLast updated on November 10th, 2024
LCM of 64 and 72
The LCM or Least Common Multiple of numbers is the smallest multiple which can be evenly divisible by each of the numbers whose LCM is to be found. LCM helps in scheduling and coordinating prices, events, also used in traffic light mechanisms, etc.
What is the LCM of 64 and 72
The LCM of 64 and 72 is 576. So, 576 is the smallest multiple shared by the numbers 64 and 72, and also 576 divides 64 and 72 evenly. We can get the exact value of LCM of 64 and 72 through various methods. Let us see how.
How to find the LCM of 64 and 72
To find the LCM of 64 and 72 we will learn some methods:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 64 and 72 Using Listing the Multiples
The Listing Multiples method is one of the methods used to find LCM of some given numbers. We have to know the multiples of the given numbers and then apply this method.
Step 1: List down the multiples of each number
Multiples of 64 = 64,128,192,256,384,448,512,576,640,.....
Multiples of 72= 72,144,216,288,360,432,504,576,648,....
Step 2 : Find out the smallest multiple from the listed multiples
The smallest common multiple is 576
Thus, LCM (64,72) = 576.
LCM of 64 and 72 Using Prime Factorization
Rule: The prime factorization of each number is to be done, and then the highest power of the prime factors are multiplied to get the LCM.
Step 1 : Find the prime factorization of the numbers:
Prime factorization of 64 = 26
Prime factorization of 72 = 23×32
Take the highest powers of each prime factor, and multiply the highest powers to
get the LCM:
32×26 = 576
LCM (64,72) = 576.
LCM of 64 and 72 Using Division Method
This is the most used method to find any LCM. It involves dividing both numbers 64 and 72 by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers
The first common prime divisors for both 64 and 72 are 2.
Step 2: Dividing 64 and 72 with 2, we get 32 and 36 respectively.
Step 3: Repeat Step 1 and 2 till both are getting perfectly divided. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
2×2×2×2×2×2×3×3 = 576
Thus, LCM (64,72) = 576
Common Mistakes and How to Avoid Them in LCM of 64 and 72
LCM of 64 and 72 Examples
Problem 1
The LCM of 64 and 72 is 576. Then what will be the LCM of 62 and 72?
Explanation
Problem 2
LCM (64,72) = x. Find the smallest positive integer (n), where n×x=1152 and the smallest positive integer (m), m× x=288
Explanation
Problem 3
What is the LCM of 64, 72 and 84?
Explanation
FAQs on LCM of 64 and 72
1.What is the LCM of 60 and 62?
2.What is the LCM of 62 and 63?
3.What is the LCM of 64,72,96,108?
4.What is the lowest multiple of 64?
5.What is the LCM of 64,72,96,112?
Important glossaries for the LCM of 64 and 72
- Prime Factor: A natural number or whole number which has factors that are 1 and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: numbers which have the only positive divisor of them both as 1.
- Relatively Prime Numbers:Numbers that have no common factors except 1.
- Multiples: The product we get when all the integers are multiplied with a particular number, one by one.
