LCM of 42 and 63
LCM of 42 and 63 is the smallest number among all common multiples of 42 and 63. The first few multiples of 42 and 63 are (42, 84, 126, 168, 210, 252, . . . ) and (63, 126, 189, 252, 315, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 63  by prime factorization, by listing multiples, and by division method.
1.  LCM of 42 and 63 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 42 and 63?
Answer: LCM of 42 and 63 is 126.
Explanation:
The LCM of two nonzero integers, x(42) and y(63), is the smallest positive integer m(126) that is divisible by both x(42) and y(63) without any remainder.
Methods to Find LCM of 42 and 63
The methods to find the LCM of 42 and 63 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 42 and 63 by Listing Multiples
To calculate the LCM of 42 and 63 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 63 (63, 126, 189, 252, 315, . . . . )
 Step 2: The common multiples from the multiples of 42 and 63 are 126, 252, . . .
 Step 3: The smallest common multiple of 42 and 63 is 126.
∴ The least common multiple of 42 and 63 = 126.
LCM of 42 and 63 by Division Method
To calculate the LCM of 42 and 63 by the division method, we will divide the numbers(42, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 63.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 63. Write this prime number(2) on the left of the given numbers(42 and 63), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (42, 63) 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 63 is the product of all prime numbers on the left, i.e. LCM(42, 63) by division method = 2 × 3 × 3 × 7 = 126.
LCM of 42 and 63 by Prime Factorization
Prime factorization of 42 and 63 is (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and (3 × 3 × 7) = 3^{2} × 7^{1} respectively. LCM of 42 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 7^{1} = 126.
Hence, the LCM of 42 and 63 by prime factorization is 126.
☛ Also Check:
 LCM of 20 and 36  180
 LCM of 14 and 20  140
 LCM of 3, 6 and 8  24
 LCM of 5, 6 and 8  120
 LCM of 8, 10 and 12  120
 LCM of 18 and 20  180
 LCM of 60 and 80  240
LCM of 42 and 63 Examples

Example 1: The GCD and LCM of two numbers are 21 and 126 respectively. If one number is 63, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 63 × a
⇒ a = (GCD × LCM)/63
⇒ a = (21 × 126)/63
⇒ a = 42
Therefore, the other number is 42. 
Example 2: Verify the relationship between GCF and LCM of 42 and 63.
Solution:
The relation between GCF and LCM of 42 and 63 is given as,
LCM(42, 63) × GCF(42, 63) = Product of 42, 63
Prime factorization of 42 and 63 is given as, 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} and 63 = (3 × 3 × 7) = 3^{2} × 7^{1}
LCM(42, 63) = 126
GCF(42, 63) = 21
LHS = LCM(42, 63) × GCF(42, 63) = 126 × 21 = 2646
RHS = Product of 42, 63 = 42 × 63 = 2646
⇒ LHS = RHS = 2646
Hence, verified. 
Example 3: Find the smallest number that is divisible by 42 and 63 exactly.
Solution:
The smallest number that is divisible by 42 and 63 exactly is their LCM.
⇒ Multiples of 42 and 63: Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, . . . .
 Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, . . . .
Therefore, the LCM of 42 and 63 is 126.
FAQs on LCM of 42 and 63
What is the LCM of 42 and 63?
The LCM of 42 and 63 is 126. To find the least common multiple of 42 and 63, we need to find the multiples of 42 and 63 (multiples of 42 = 42, 84, 126, 168; multiples of 63 = 63, 126, 189, 252) and choose the smallest multiple that is exactly divisible by 42 and 63, i.e., 126.
If the LCM of 63 and 42 is 126, Find its GCF.
LCM(63, 42) × GCF(63, 42) = 63 × 42
Since the LCM of 63 and 42 = 126
⇒ 126 × GCF(63, 42) = 2646
Therefore, the greatest common factor (GCF) = 2646/126 = 21.
Which of the following is the LCM of 42 and 63? 11, 45, 40, 126
The value of LCM of 42, 63 is the smallest common multiple of 42 and 63. The number satisfying the given condition is 126.
What is the Relation Between GCF and LCM of 42, 63?
The following equation can be used to express the relation between GCF and LCM of 42 and 63, i.e. GCF × LCM = 42 × 63.
How to Find the LCM of 42 and 63 by Prime Factorization?
To find the LCM of 42 and 63 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (63 = 3 × 3 × 7). LCM of 42 and 63 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 63.
⇒ LCM of 42, 63 = 2^{1} × 3^{2} × 7^{1} = 126.