LCM of 148 and 185

LCM of 148 and 185 is the smallest number among all common multiples of 148 and 185. The first few multiples of 148 and 185 are (148, 296, 444, 592, 740, 888, . . . ) and (185, 370, 555, 740, 925, 1110, . . . ) respectively. There are 3 commonly used methods to find LCM of 148 and 185 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 148 and 185 is 740.

Explanation:

The LCM of two non-zero integers, x(148) and y(185), is the smallest positive integer m(740) that is divisible by both x(148) and y(185) without any remainder.

Let's look at the different methods for finding the LCM of 148 and 185.

• By Division Method
• By Listing Multiples
• By Prime Factorization Method

LCM of 148 and 185 by Division Method

To calculate the LCM of 148 and 185 by the division method, we will divide the numbers(148, 185) by their prime factors (preferably common). The product of these divisors gives the LCM of 148 and 185.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 148 and 185. Write this prime number(2) on the left of the given numbers(148 and 185), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (148, 185) 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 148 and 185 is the product of all prime numbers on the left, i.e. LCM(148, 185) by division method = 2 × 2 × 5 × 37 = 740.

LCM of 148 and 185 by Listing Multiples

To calculate the LCM of 148 and 185 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 148 (148, 296, 444, 592, 740, 888, . . . ) and 185 (185, 370, 555, 740, 925, 1110, . . . . )
• Step 2: The common multiples from the multiples of 148 and 185 are 740, 1480, . . .
• Step 3: The smallest common multiple of 148 and 185 is 740.

∴ The least common multiple of 148 and 185 = 740.

LCM of 148 and 185 by Prime Factorization

Prime factorization of 148 and 185 is (2 × 2 × 37) = 2² × 37¹ and (5 × 37) = 5¹ × 37¹ respectively. LCM of 148 and 185 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ × 37¹ = 740.
Hence, the LCM of 148 and 185 by prime factorization is 740.

☛ Also Check:

• LCM of 45 and 63 - 315
• LCM of 45 and 60 - 180
• LCM of 45 and 54 - 270
• LCM of 45 and 50 - 450
• LCM of 45 and 120 - 360
• LCM of 42 and 72 - 504
• LCM of 42 and 70 - 210

FAQs on LCM of 148 and 185

What is the LCM of 148 and 185?

The LCM of 148 and 185 is 740. To find the least common multiple of 148 and 185, we need to find the multiples of 148 and 185 (multiples of 148 = 148, 296, 444, 592 . . . . 740; multiples of 185 = 185, 370, 555, 740) and choose the smallest multiple that is exactly divisible by 148 and 185, i.e., 740.

If the LCM of 185 and 148 is 740, Find its GCF.

LCM(185, 148) × GCF(185, 148) = 185 × 148
Since the LCM of 185 and 148 = 740
⇒ 740 × GCF(185, 148) = 27380
Therefore, the GCF = 27380/740 = 37.

What is the Relation Between GCF and LCM of 148, 185?

The following equation can be used to express the relation between GCF and LCM of 148 and 185, i.e. GCF × LCM = 148 × 185.

Which of the following is the LCM of 148 and 185? 35, 28, 740, 42

The value of LCM of 148, 185 is the smallest common multiple of 148 and 185. The number satisfying the given condition is 740.

How to Find the LCM of 148 and 185 by Prime Factorization?

To find the LCM of 148 and 185 using prime factorization, we will find the prime factors, (148 = 2 × 2 × 37) and (185 = 5 × 37). LCM of 148 and 185 is the product of prime factors raised to their respective highest exponent among the numbers 148 and 185.
⇒ LCM of 148, 185 = 2² × 5¹ × 37¹ = 740.