LCM of 42 and 72
LCM of 42 and 72 is the smallest number among all common multiples of 42 and 72. The first few multiples of 42 and 72 are (42, 84, 126, 168, 210, 252, . . . ) and (72, 144, 216, 288, 360, 432, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 72  by division method, by listing multiples, and by prime factorization.
1.  LCM of 42 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 42 and 72?
Answer: LCM of 42 and 72 is 504.
Explanation:
The LCM of two nonzero integers, x(42) and y(72), is the smallest positive integer m(504) that is divisible by both x(42) and y(72) without any remainder.
Methods to Find LCM of 42 and 72
Let's look at the different methods for finding the LCM of 42 and 72.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 42 and 72 by Listing Multiples
To calculate the LCM of 42 and 72 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, 252, . . . ) and 72 (72, 144, 216, 288, 360, 432, . . . . )
 Step 2: The common multiples from the multiples of 42 and 72 are 504, 1008, . . .
 Step 3: The smallest common multiple of 42 and 72 is 504.
∴ The least common multiple of 42 and 72 = 504.
LCM of 42 and 72 by Division Method
To calculate the LCM of 42 and 72 by the division method, we will divide the numbers(42, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 72.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 72. Write this prime number(2) on the left of the given numbers(42 and 72), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (42, 72) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 42 and 72 is the product of all prime numbers on the left, i.e. LCM(42, 72) by division method = 2 × 2 × 2 × 3 × 3 × 7 = 504.
LCM of 42 and 72 by Prime Factorization
Prime factorization of 42 and 72 is (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and (2 × 2 × 2 × 3 × 3) = 2^{3} × 3^{2} respectively. LCM of 42 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{2} × 7^{1} = 504.
Hence, the LCM of 42 and 72 by prime factorization is 504.
☛ Also Check:
 LCM of 4 and 12  12
 LCM of 80 and 120  240
 LCM of 3 and 1  3
 LCM of 54 and 90  270
 LCM of 5, 8 and 15  120
 LCM of 72 and 96  288
 LCM of 3 and 11  33
LCM of 42 and 72 Examples

Example 1: Verify the relationship between GCF and LCM of 42 and 72.
Solution:
The relation between GCF and LCM of 42 and 72 is given as,
LCM(42, 72) × GCF(42, 72) = Product of 42, 72
Prime factorization of 42 and 72 is given as, 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and 72 = (2 × 2 × 2 × 3 × 3) = 2^{3} × 3^{2}
LCM(42, 72) = 504
GCF(42, 72) = 6
LHS = LCM(42, 72) × GCF(42, 72) = 504 × 6 = 3024
RHS = Product of 42, 72 = 42 × 72 = 3024
⇒ LHS = RHS = 3024
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 6 and 504 respectively. If one number is 42, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 42 × y
⇒ y = (GCD × LCM)/42
⇒ y = (6 × 504)/42
⇒ y = 72
Therefore, the other number is 72. 
Example 3: Find the smallest number that is divisible by 42 and 72 exactly.
Solution:
The smallest number that is divisible by 42 and 72 exactly is their LCM.
⇒ Multiples of 42 and 72: Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, . . . .
 Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, . . . .
Therefore, the LCM of 42 and 72 is 504.
FAQs on LCM of 42 and 72
What is the LCM of 42 and 72?
The LCM of 42 and 72 is 504. To find the LCM (least common multiple) of 42 and 72, we need to find the multiples of 42 and 72 (multiples of 42 = 42, 84, 126, 168 . . . . 504; multiples of 72 = 72, 144, 216, 288 . . . . 504) and choose the smallest multiple that is exactly divisible by 42 and 72, i.e., 504.
What is the Relation Between GCF and LCM of 42, 72?
The following equation can be used to express the relation between GCF and LCM of 42 and 72, i.e. GCF × LCM = 42 × 72.
If the LCM of 72 and 42 is 504, Find its GCF.
LCM(72, 42) × GCF(72, 42) = 72 × 42
Since the LCM of 72 and 42 = 504
⇒ 504 × GCF(72, 42) = 3024
Therefore, the GCF (greatest common factor) = 3024/504 = 6.
How to Find the LCM of 42 and 72 by Prime Factorization?
To find the LCM of 42 and 72 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (72 = 2 × 2 × 2 × 3 × 3). LCM of 42 and 72 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 72.
⇒ LCM of 42, 72 = 2^{3} × 3^{2} × 7^{1} = 504.
What are the Methods to Find LCM of 42 and 72?
The commonly used methods to find the LCM of 42 and 72 are:
 Prime Factorization Method
 Listing Multiples
 Division Method