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Chapter 4: Integers and Number Theory
4.5 GCD and LCM
4.5.1. Vocabulary
4.5.1.1. GCD – greatest common divisor, often called the GCF or greatest
common factor: largest factor for a pair or group of numbers
4.5.2. Find the GCF between 324 and 432
2|324 432
2|162 216
3| 81 108
3| 27 36
3| 9 12
3
4
GCF = 2 x 2 x 3 x 3 x 3 = 22 x 33 = 4 x 27 = 108
Check: 324/108 = 3; 432/108 = 4
4.5.2.1. LCM – least common multiple: smallest common multiple of 2 or
more numbers
4.5.3. Find the LCM between 324 and 432
2|324 432
2|162 216
3| 81 108
3| 27 36
3| 9 12
3
4
LCM = 2 x 2 x 3 x 3 x 3 x 3 x 4 = 24 x 34 = 16 x 81 = 1296
Check: 1296/324 = 4; 1296/432 = 3
Check: GCF x LCM = ab; 108 x 1296 = 139968
Note: A common multiple can always be found by multiplying any
two numbers together: 324 x 432 = 139968. This number is the
LCM only when the numbers involved are relatively prime or prime.
In general it is NOT the LCM.
4.5.3.1. Now try this : Discuss in your groups
4.5.3.1.1. Find the GCF and LCM of the following groups of numbers
4.5.3.1.1.1.
55, 110
4.5.3.1.1.2.
92, 78
4.5.3.1.1.3.
4620, 2940, 1260
4.5.4. Ongoing Assessment p. 251
4.5.4.1. Home work: 1a, 1c, 2a, 2c, 3a, 4a, 13