LCM of 24 and 42
LCM of 24 and 42 is the smallest number among all common multiples of 24 and 42. The first few multiples of 24 and 42 are (24, 48, 72, 96, 120, 144, . . . ) and (42, 84, 126, 168, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 42  by division method, by listing multiples, and by prime factorization.
1.  LCM of 24 and 42 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 24 and 42?
Answer: LCM of 24 and 42 is 168.
Explanation:
The LCM of two nonzero integers, x(24) and y(42), is the smallest positive integer m(168) that is divisible by both x(24) and y(42) without any remainder.
Methods to Find LCM of 24 and 42
The methods to find the LCM of 24 and 42 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 24 and 42 by Prime Factorization
Prime factorization of 24 and 42 is (2 × 2 × 2 × 3) = 2^{3} × 3^{1} and (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1} respectively. LCM of 24 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{1} × 7^{1} = 168.
Hence, the LCM of 24 and 42 by prime factorization is 168.
LCM of 24 and 42 by Division Method
To calculate the LCM of 24 and 42 by the division method, we will divide the numbers(24, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 42.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 42. Write this prime number(2) on the left of the given numbers(24 and 42), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (24, 42) 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 24 and 42 is the product of all prime numbers on the left, i.e. LCM(24, 42) by division method = 2 × 2 × 2 × 3 × 7 = 168.
LCM of 24 and 42 by Listing Multiples
To calculate the LCM of 24 and 42 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 24 (24, 48, 72, 96, 120, 144, . . . ) and 42 (42, 84, 126, 168, 210, . . . . )
 Step 2: The common multiples from the multiples of 24 and 42 are 168, 336, . . .
 Step 3: The smallest common multiple of 24 and 42 is 168.
∴ The least common multiple of 24 and 42 = 168.
☛ Also Check:
 LCM of 21 and 42  42
 LCM of 207 and 138  414
 LCM of 3, 4 and 8  24
 LCM of 45 and 120  360
 LCM of 60, 84 and 108  3780
 LCM of 72 and 108  216
 LCM of 5, 10, 15 and 20  60
LCM of 24 and 42 Examples

Example 1: Verify the relationship between GCF and LCM of 24 and 42.
Solution:
The relation between GCF and LCM of 24 and 42 is given as,
LCM(24, 42) × GCF(24, 42) = Product of 24, 42
Prime factorization of 24 and 42 is given as, 24 = (2 × 2 × 2 × 3) = 2^{3} × 3^{1} and 42 = (2 × 3 × 7) = 2^{1} × 3^{1} × 7^{1}
LCM(24, 42) = 168
GCF(24, 42) = 6
LHS = LCM(24, 42) × GCF(24, 42) = 168 × 6 = 1008
RHS = Product of 24, 42 = 24 × 42 = 1008
⇒ LHS = RHS = 1008
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 6 and 168 respectively. If one number is 42, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 42 × m
⇒ m = (GCD × LCM)/42
⇒ m = (6 × 168)/42
⇒ m = 24
Therefore, the other number is 24. 
Example 3: Find the smallest number that is divisible by 24 and 42 exactly.
Solution:
The smallest number that is divisible by 24 and 42 exactly is their LCM.
⇒ Multiples of 24 and 42: Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
 Multiples of 42 = 42, 84, 126, 168, 210, . . . .
Therefore, the LCM of 24 and 42 is 168.
FAQs on LCM of 24 and 42
What is the LCM of 24 and 42?
The LCM of 24 and 42 is 168. To find the LCM of 24 and 42, we need to find the multiples of 24 and 42 (multiples of 24 = 24, 48, 72, 96 . . . . 168; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 24 and 42, i.e., 168.
What is the Relation Between GCF and LCM of 24, 42?
The following equation can be used to express the relation between GCF and LCM of 24 and 42, i.e. GCF × LCM = 24 × 42.
What is the Least Perfect Square Divisible by 24 and 42?
The least number divisible by 24 and 42 = LCM(24, 42)
LCM of 24 and 42 = 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 24 and 42 = LCM(24, 42) × 2 × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.
If the LCM of 42 and 24 is 168, Find its GCF.
LCM(42, 24) × GCF(42, 24) = 42 × 24
Since the LCM of 42 and 24 = 168
⇒ 168 × GCF(42, 24) = 1008
Therefore, the GCF (greatest common factor) = 1008/168 = 6.
Which of the following is the LCM of 24 and 42? 24, 2, 18, 168
The value of LCM of 24, 42 is the smallest common multiple of 24 and 42. The number satisfying the given condition is 168.
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