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lcm(30,50,60)This solution deals with the least common multiple (LCM) by prime factorization. Find the prime factors of 30 The prime factors of 30 are 2, 3 and 5. Find the prime factors of 50The prime factors of 50 are 2, 5 and 5. Find the prime factors of 60The prime factors of 60 are 2, 2, 3 and 5. Build a prime factors tableDetermine the maximum number of times each prime factor (2, 3, 5) occurs in the factorization of the given numbers:
The prime factor 3 occurs one time, while 2 and 5 occur more than once. Calculate the LCMThe least common multiple is the product of all factors in the greatest number of their occurrence. LCM = LCM = LCM = 300 The least common multiple of 30, 50 and 60 is 300. Why learn thisThe least common multiple (LCM), sometimes called the lowest common multiple or least common divisor, is helpful for understanding the relationships between numbers. For example, if it takes Earth 365 days to orbit the sun and it takes Venus 225 days to orbit the sun and both are in perfect alignment at the time this scenario is given, how long will it take for Earth and Venus to align again? We can use LCM to determine that the answer would be 16,425 days. LCM is also a very important part of many mathematical concepts that also have real-world applications. For example, we use LCMs when adding and subtracting fractions, which we use quite frequently. Terms and topicsRelated linksOther solution types
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 50. First we will calculate the prime factors of 30 and 50. Prime Factorization of 30 Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is: 30 = 21×31×51 Prime Factorization of 50 Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is: 50 = 21×52 Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 50. LCM(30,50)
= 21×31×52 Factors of 30 List of positive integer factors of 30 that divides 30 without a remainder. 1, 2, 3, 5, 6, 10, 15, 30 Factors of 50 List of positive integer factors of 50 that divides 50 without a remainder. 1, 2, 5, 10, 25, 50
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(30,50) = 10 (i) The LCM of 50 and 30 is associative LCM of 30 and 50 = LCM of 50 and 30 1. What is the LCM of 30 and 50? Answer: LCM of 30 and 50 is 150. 2. What are the Factors of 30? Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30. 3. What are the Factors of 50? Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50. 4. How to Find the LCM of 30 and 50? Answer: Least Common Multiple of 30 and 50 = 150 Step 1: Find the prime factorization of 30 30 = 2 x 3 x 5 Step 2: Find the prime factorization of 50 50 = 2 x 5 x 5 Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm: LCM = 150 = 2 x 3 x 5 x 5 Step 4: Therefore, the least common multiple of 30 and 50 is 150. What is the LCM 30 40 and 50?Answer: LCM of 30, 40, 50 is 600.
What is the LCM of 30?The LCM of 30 and 36 is 180. To find the LCM of 30 and 36, we need to find the multiples of 30 and 36 (multiples of 30 = 30, 60, 90, 120 . . . . 180; multiples of 36 = 36, 72, 108, 144 . . . . 180) and choose the smallest multiple that is exactly divisible by 30 and 36, i.e., 180.
What is the least common multiple of 20 and 50?The LCM of 20 and 50 is 100.
What is the LCM of 50?To find the LCM of 50 and 100 using prime factorization, we will find the prime factors, (50 = 2 × 5 × 5) and (100 = 2 × 2 × 5 × 5). LCM of 50 and 100 is the product of prime factors raised to their respective highest exponent among the numbers 50 and 100. ⇒ LCM of 50, 100 = 22 × 52 = 100.
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What is the least common multiple of 30 and 50
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