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Given that the LCM of 306 and 657 is 22338, What is the LCM of 102 306 and 657?
The LCM of 306 and 657 is 22338. The LCM of 102, 306, and 657 is the same as the LCM of 306 and 657.
We are given that the LCM of 306 and 657 is 22338.
We are asked to find the LCM of 102, 306, and 657.
Since 306 is a multiple of 102 (306 = 2 * 102), the LCM of 102 and 306 is simply 306.
Therefore, the LCM of 102, 306, and 657 is the same as the LCM of 306 and 657, which is 22338.
Here’s another way to think about it: the LCM of a set of numbers is the least common multiple of all the numbers in the set. Since any multiple of the LCM of two numbers is also a multiple of each individual number, the LCM of 306 and 657 must also be a multiple of 102.
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Therefore, the LCM of 102, 306, and 657 is the same as the LCM of 306 and 657.
What is LCM and HCF?
LCM (Least Common Multiple) and HCF (Highest Common Factor), also known as GCD (Greatest Common Divisor), are two fundamental concepts in arithmetic.
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Least Common Multiple (LCM): The least common multiple of two or more integers is the smallest positive integer that is divisible by each of the given integers without leaving a remainder. For example, the least common multiple of 4 and 6 is 12 because 12 is the smallest number that is divisible by both 4 and 6.
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Highest Common Factor (HCF): The highest common factor of two or more integers is the largest positive integer that divides each of the given integers without leaving a remainder. For example, the highest common factor of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 without leaving a remainder.
These concepts are often used in various mathematical operations, such as simplifying fractions, solving equations, and finding common denominators.
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