lcm 6,9

{ "query": { "display": "lcm $$6,\\:9$$", "symbolab_question": "PRE_ALGEBRA#lcm 6,9" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Factors & Primes", "subTopic": "LCM", "default": "18", "meta": { "showVerify": true } }, "methods": [ { "method": "Solve using prime factors", "query": { "display": "lcm by prime factors $$6,\\:9$$", "symbolab_question": "lcmfact 6,9" } }, { "method": "Solve using multipliers", "query": { "display": "lcm by multipliers $$6,\\:9$$", "symbolab_question": "lcmmult 6,9" } }, { "method": "Solve using GCD", "query": { "display": "lcm by gcd $$6,\\:9$$", "symbolab_question": "lcmgcd 6,9" } } ], "steps": { "type": "interim", "title": "Least Common Multiplier of $$6,\\:9:{\\quad}18$$", "input": "6,\\:9", "steps": [ { "type": "definition", "title": "Least Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b$$ is the smallest positive number that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Prime factorization of $$6:{\\quad}2\\cdot\\:3$$", "input": "6", "steps": [ { "type": "step", "primary": "$$6\\:$$divides by $$2\\quad\\:6=3\\cdot\\:2$$", "result": "=2\\cdot\\:3" }, { "type": "step", "primary": "$$2,\\:3$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:3" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRuUHkFwKrCGUG/pR2kioRow/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1AjXz67i9oO9i25G22wINi" } }, { "type": "interim", "title": "Prime factorization of $$9:{\\quad}3\\cdot\\:3$$", "input": "9", "steps": [ { "type": "step", "primary": "$$9\\:$$divides by $$3\\quad\\:9=3\\cdot\\:3$$", "result": "=3\\cdot\\:3" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRjcq2F6aCU5dakzncJqkgGc/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp02ygGGsmIGE3wDrLHDVisx" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$6$$ or $$9$$", "result": "=2\\cdot\\:3\\cdot\\:3" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:3\\cdot\\:3=18$$", "result": "=18" } ], "meta": { "solvingClass": "LCM" } }, "meta": { "showVerify": true } }