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Lesson 10: Least common multiple

# Least common multiple: repeating factors

To find the Least Common Multiple (LCM) of two integers, follow these steps: 1) Find the prime factorization of both numbers. 2) Determine which prime factors are needed for the least common multiple (LCM) to be divisible by both numbers. 3) Multiply the necessary prime factors together to get the least common multiple (LCM). Created by Sal Khan.

## Want to join the conversation?

• how is the gcf different from the lcm
• The gcf is the LARGEST number that WILL DIVIDE INTO both given numbers.
As such, it will be less than at least one (usually both) of the given numbers.
The lcm is the SMALLEST number that BOTH GIVEN NUMBERS DIVIDE into.
As such, it will be greater than at least one (often both) of the given numbers.
• what is the greatest common factor of 120 and 192
• First, let's list out the factor pairs of each number.
``120: 1 and 120; 2 and 60; 3 and 40; 4 and 30; 5 and 24; 6 and 20; 8 and 15; 10 and 12192: 1 and 192; 2 and 96; 3 and 64; 4 and 48; 6 and 32; 8 and 24; 12 and 16``

Next, let's order the factors of each number from least to greatest.
``120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24 30, 40, 60, 120192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192``

Based on these two lists, let's make a list of all of the common factors of 120 and 192.
`120 and 192: 1, 2, 3, 4, 6, 8, 12, 24`
The GCF of 120 and 192 is the greatest value in this list, which is 24.
• what is that fancy bracket that Sal draws around the 2*3*5 at called, if it is called anything other than a bracket?
• A bracket is [ or ] . A brace is { or } . I guess you can call it a squiggly line that connects the selected objects and relates them to something else in the part that sticks out in the middle.
• when i watched the video, i got confused because i keep trying to do it but i keep getting the answers wrong can you help me more?
• What is the prime factoring
• what is the least common multiplies of 144 and 38?
• 144 = 12*12=3*2*2*3*2*2
38=2*19, so since they only have a 2 in common, multiply 144*19 to get the LCM (the 2 in 38 will not repeat).
• can there be one repeating factor number than two repeating number numbers ?
• What does a whole number with a line over it mean?
• I've never seen that notation. But here are some possible meanings:
(1) Someone didn't write a repeating decimal correctly. 6.666666 should be written as 6.6 with a bar or the .6 portion.
(2) Someone forgot to write the top portion of a fraction.
(3) I've read that it can be a VERY rarely used way of indicating "average". So a 3 with a line over it would indicate that 3 is the average of the data set {1,2,3,4,5}.